Verifying the Conditions for Conducting a Chi-Square Test for Homogeneity are Met

• 1.

A certain type of fruit-flavored candy is advertised to be uniformly distributed. A simple random sample of 300 pieces of candy were obtained and 75 were sour apple, 70 were mango, 73 were blue raspberry, and 82 were orange. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 2.

A soccer coach claims that the age of the players on his team is evenly distributed. A simple random sample of 30 players from his team were taken and it was found that 9 players were thirteen years old, 13 players were fourteen years old, and 8 players were fifteen years old. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 3.

A bakery claims that 50% of its customers buy muffins when they come to make a purchase. A simple random sample of 90 customers was taken and 49 customers bought a muffin. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 4.

A school teacher made gift bags full of chocolates for her students and claims that the types of chocolates are uniformly distributed throughout the bags. A simple random sample of 200 chocolates from the bags were obtained and it was found that 45 were peanut butter cups, 53 were chocolate caramels, 54 were coconut filled, and 48 were cream filled. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 5.

A trading card company claims that 55% of their cards printed are common cards, 40% are uncommon, and 5% are rare. A simple random sample of 100 cards from the company was obtained and 60 were common, 37 were uncommon, and 3 were rare. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 6.

A certain type of colored candy is advertised to be uniformly distributed. A simple random sample of 150 pieces of candy were obtained and 52 were red, 51 were blue, and 47 were green. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 7.

A baseball coach claims that the experience level of the players on his team is evenly distributed (no experience, one year of experience, more than one year of experience). A sample of 25 players from his team were taken and it was found that 7 players had no experience, 8 players had one year of experience, and 10 players had more than one year of experience. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 8.

A grocery store claims that 75% of its customers buy a gallon of milk when they shop at their store. A simple random sample of 120 customers was taken and 83 customers bought a gallon of milk. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 9.

A company made gift bags full of fruits for its employees and claims that the types of fruit are uniformly distributed throughout the bags. A simple random sample of 50 fruits from the bags were obtained and it was found that 10 were apples, 12 were oranges, 8 were peaches, 13 were plums, and 7 were lemons. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 10.

A blind bag toy company claims that 60% of their bags contain common toy figures, 25% are uncommon, and 15% are rare. A sample of 100 blind bags from the company was taken and opened and 62 were common, 23 were uncommon, and 15 were rare. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 11.

A certain type of nut mix is advertised to be uniformly distributed between cashews, almonds, peanuts, and pistachios. A simple random sample of 200 nuts was obtained and 42 were cashews, 40 were almonds, 65 were peanuts, and 53 were pistachios. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 12.

A tennis coach claims that the experience level of the players on his team is evenly distributed (no experience, one to two years of experience, and more than two years of experience). A simple random sample of 12 players from his team were taken and it was found that 2 players had no experience, 2 players had one to two years of experience, and 8 players had more than two years of experience. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 13.

A movie theater claims that 80% of its customers buy a bag of popcorn when they come to see a movie. A simple random sample of 140 customers was taken and 105 customers bought a bag of popcorn. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 14.

A college professor made gift bags full of school supplies for her students and claims that the types school supplies were uniformly distributed throughout the bags. A simple random sample of 60 supplies from the bags were obtained and it was found that 20 were pencils, 15 were notebooks, and 25 were pens. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 15.

A baseball card company claims that 50% of their cards printed feature all-star players, 30% feature veteran players, and 20% feature rookie players. A simple random sample of 200 cards from the company was obtained and 105 were all-stars, 54 were veterans, and 41 were rookies. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 16.

A certain type of flavored candy is advertised to be uniformly distributed. A sample of 250 pieces of candy were obtained and 60 were peppermint, 45 were fruit punch, 52 were cinnamon, 56 were chocolate, and 37 were caramel. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 17.

A football coach claims that the age of the players on his team is evenly distributed. A simple random sample of 12 players from his team were taken and it was found that 4 players were sixteen years old, 5 players were seventeen years old, and 3 players were eighteen years old. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 18.

A museum claims that 45% of its visitors stay in the museum for at least an hour before leaving. A simple random sample of 100 visitors was taken and 39 of them stayed in the museum for at least an hour before leaving. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 19.

A language arts teacher made gift bags full of short books for her students and claims that the genre of books are uniformly distributed throughout the bags. A sample of 70 books from the bags were obtained and it was found that 20 books were mystery novels, 25 were adventure novels, and 25 were nonfiction. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 20.

A video game company claims that 50% of the rewards from their loot boxes are cosmetic items, 40% are unlockable features in the game, and 10% give in-game currency. A simple random sample of 150 loot boxes in the company's game was opened and 78 were cosmetic items, 58 were unlockable features, and 14 gave in-game currency. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 21.

A certain type of fruit-flavored candy is advertised to be uniformly distributed. A sample of 400 pieces of candy were obtained and 95 were cherry, 105 were watermelon, 100 were black raspberry, and 100 were lemon. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• 22.

A hockey coach claims that the number of goals scored by the players on his team in the previous season is evenly distributed. A simple random sample of 20 players from his team were taken and it was found that 5 players scored one goal, 7 players scored two goals, 4 players scored three goals, and 4 players scored more than three goals. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 23.

A pizzeria claims that 65% of its customers order a large pizza over a small pizza when they order a pizza. A simple random sample of 130 customers was taken and 92 customers ordered a large pizza instead of a small pizza. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 24.

A company made gift bags full of chocolates for its employees and claims that the types of chocolates are uniformly distributed throughout the bags. A simple random sample of 90 chocolates from the bags were obtained and it was found that 33 were white chocolate bars, 27 were dark chocolate bars, and 30 were regular chocolate bars. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 25.

A teacher claims that 50% of their students say gym is their favorite class, 25% say it is math, and 25% say it is science. A sample of 250 students are taken and 125 said their favorite class was gym, 65 said math, and 60 said science. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• 26.

A certain type of colored candy is advertised to be uniformly distributed. A sample of 500 pieces of candy were obtained and 108 were black, 99 were white, 97 were purple, 112 were brown, and 84 were magenta. Verify that the conditions for conducting a chi-square test for homogeneity are met for this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 27.

A soccer coach claims that the number of goals scored by each of the players on his team in the past season is evenly distributed. A simple random sample of 24 players from his team were taken and it was found that 5 players scored no goals, 6 players scored one goal, 6 player scored two goals, 5 players scored three goals, and 2 players scored more than three goals. If a chi-square test for homogeneity was to be conducted, are the conditions met in this scenario?

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 28.

A lawyer claims that 90% of his clients are satisfied with his services. A simple random sample of 110 clients was surveyed and 101 clients said that they were satisfied with his services. Are the conditions for a chi-square test for homogeneity met in this scenario if one was to be conducted?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• 29.

A bus driver made gift bags full of candy for the students that ride on her bus and claims that the types of candy are uniformly distributed throughout the bags. A sample of 150 pieces of candy from the bags were obtained and it was found that 52 were fruit-flavored candy, 60 were chocolate-flavored candy, and 38 were peppermint-flavored candy. Given this information, are the conditions for a chi-square test for homogeneity met in this scenario?

• The variable in this study is categorial, the number of sample observations in each category is at least 5, and the sample was simple and randomly selected. So, all conditions are met in this scenario.

• The variable in this study is categorial, but the number of sample observations in each category is not at least 5, so not all conditions are met in this scenario.

• The variable in this study is categorial and the number of sample observations in each category is at least 5, but it is unknown if the sample is simple and randomly selected. So, not all conditions are met.

• The sample in this study was simple and randomly selected, but the variable is not categorial. So, not all conditions are met in this scenario.

• 30.

A mobile video game company claims that 75% of its player base is free-to-play, 20% have spent between $1 and$100 on the game, and 5% have spent more than $100 on the game. A simple random sample of 1000 players of the mobile game was taken and 804 were free-to-play, 158 spent between$1 and $100 on the game, and 38 spent more than$100. A researcher is interested in conducting a chi-square test for homogeneity for this scenario. Are all the conditions for this test met?