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Making Valid Conclusions about a Hypothesis Test for a Mean

  • 1.

    A career analyst believes that the mean salary for plumbers has risen from the current mean of $75,000. To test their hypothesis, a simple random sample of plumbers is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.035. Make a valid conclusion based on this p-value.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst cannot conclude that the mean salary for plumbers did rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for plumbers did rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for plumbers did not rise from the current mean.

  • 2.

    A school district believes that the mean number of students who fail their calculus course each year has risen from the current mean of 4 students. To test their hypothesis, a simple random sample of students is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.043. Based on this p-value, what conclusion can be made?

    Answers:

    • At the 5% level, the school district cannot conclude that the mean number of students who fail their calculus course each year did rise from the current mean.

    • At the 5% level, the school district can conclude that the mean number of students who fail their calculus course each year did not rise from the current mean.

    • At the 5% level, the school district can conclude that the mean number of students who fail their calculus course each year did rise from the current mean.

    • No conclusion can be made based on the given p-value.

  • 3.

    A soccer coach believes that the mean number of goals his team scores in a game has risen from the current mean of 2 goals. To test the hypothesis, a simple random sample of games is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.125. What conclusion can be made based on this p-value?

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach can conclude that the mean number of goals scored in a game decreased from the current mean.

    • At the 10% level, the coach cannot conclude that the mean number of goals scored in a game increased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of goals scored in a game increased from the current mean.

  • 4.

    A bakery believes that the mean number of pastry sales per day has risen from the current mean of 120 pastries. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.233. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the bakery can conclude that the mean number of pastries sold per day decreased from the current mean.

    • At the 10% level, the bakery can conclude that the mean number of pastries sold per day increased from the current mean.

    • At the 10% level, the bakery cannot conclude that the mean number of pastries sold per day increased from the current mean.

  • 5.

    A fisherman believes that since he started using a new type of bait, the mean number of fish he catches every day has risen from the current mean of 25 fish. To test the hypothesis, a simple random sample of days is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.022. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • At the 3% level, the fisherman can conclude that the mean number of fish caught per day decreased from the current mean.

    • At the 3% level, the fisherman can conclude that the mean number of fish caught per day increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 3% level, the fisherman cannot conclude that the mean number of fish caught per day increased from the current mean.

  • 6.

    A career analyst believes that the mean salary for accountants has declined from the current mean of $85,000. To test their hypothesis, a simple random sample of accountants is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.063. Make a valid conclusion based on this p-value.

    Answers:

    • At the 5% level, the career analyst can conclude that the mean salary for accountants did decline from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst can conclude that the mean salary for accountants did not decline from the current mean.

    • At the 5% level, the career analyst cannot conclude that the mean salary for accountants did decline from the current mean.

  • 7.

    A school district believes that the mean number of students who pass their physics course each year has risen from the current mean of 90 students. To test their hypothesis, a simple random sample of students is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.012. Based on this p-value, what conclusion can be made?

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the school district can conclude that the mean number of students who pass their physics course each year did not rise from the current mean.

    • At the 5% level, the school district cannot conclude that the mean number of students who pass their physics course each year did rise from the current mean.

    • At the 5% level, the school district can conclude that the mean number of students who pass their physics course each year did rise from the current mean.

  • 8.

    A basketball coach believes that the mean number of three point shots his team makes in a game has risen from the current mean of 10 three point shots. To test the hypothesis, a simple random sample of games is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.358. What conclusion can be made based on this p-value?

    Answers:

    • At the 10% level, the coach cannot conclude that the mean number of three point shots scored in a game increased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of three point shots scored in a game increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach can conclude that the mean number of three point shots scored in a game decreased from the current mean.

  • 9.

    A coffee shop believes that the mean number of cups of coffee sold per day has declined from the current mean of 250 cups of coffee. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.089. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coffee shop can conclude that the mean number of coffee cups sold per day increased from the current mean.

    • At the 10% level, the coffee shop can conclude that the mean number of coffee cups sold per day decreased from the current mean.

    • At the 10% level, the coffee shop cannot conclude that the mean number of coffee cups sold per day decreased from the current mean.

  • 10.

    A mechanic believes that since he started using a new tool, the mean amount of time it takes him to complete a project has declined from the current mean of 30 minutes. To test the hypothesis, a simple random sample of projects is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.056. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • At the 3% level, the mechanic can conclude that the mean amount of time to complete a project has increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 3% level, the mechanic cannot conclude that the mean amount of time to complete a project has decreased from the current mean.

    • At the 3% level, the mechanic can conclude that the mean amount of time to complete a project has decreased from the current mean.

  • 11.

    A career analyst believes that the mean salary for teachers has risen from the current mean of $56,000. To test their hypothesis, a simple random sample of teachers is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.072. Make a valid conclusion based on this p-value.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst can conclude that the mean salary for teachers did not rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for teachers did rise from the current mean.

    • At the 5% level, the career analyst cannot conclude that the mean salary for teachers did rise from the current mean.

  • 12.

    A school district believes that the mean number of students who pass the standardized exams each year has risen from the current mean of 325 students. To test their hypothesis, a simple random sample of students is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.015. Based on this p-value, what conclusion can be made?

    Answers:

    • At the 5% level, the school district can conclude that the mean number of students who pass the standardized exams each year did not rise from the current mean.

    • At the 5% level, the school district cannot conclude that the mean number of students who pass the standardized exams each year did rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the school district can conclude that the mean number of students who pass the standardized exams each year did rise from the current mean.

  • 13.

    A football coach believes that the mean number of games won in a season by his team has risen from the current mean of 4 wins. To test the hypothesis, a simple random sample of football seasons is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.180. What conclusion can be made based on this p-value?

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach can conclude that the mean number of games won in a season increased from the current mean.

    • At the 10% level, the coach cannot conclude that the mean number of games won in a season increased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of games won in a season decreased from the current mean.

  • 14.

    A small pizzeria believes that the mean number of pizzas per day has risen from the current mean of 80 pizzas. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.064. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • At the 10% level, the pizzeria can conclude that the mean number of pizzas sold per day decreased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the pizzeria can conclude that the mean number of pizzas sold per day increased from the current mean.

    • At the 10% level, the pizzeria cannot conclude that the mean number of pizzas sold per day increased from the current mean.

  • 15.

    A scuba diver believes that since he started using a new air tank, the mean number of minutes he can spend underwater per dive has risen from the current mean of 65 minutes. To test the hypothesis, a simple random sample of dives is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.055. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 3% level, the scuba diver cannot conclude that the mean number of minutes he can spend underwater per dive increased from the current mean.

    • At the 3% level, the scuba diver can conclude that the mean number of minutes he can spend underwater per dive increased from the current mean.

    • At the 3% level, the scuba diver can conclude that the mean number of minutes he can spend underwater per dive decreased from the current mean.

  • 16.

    A career analyst believes that the mean salary for welders has risen from the current mean of $90,000. To test their hypothesis, a simple random sample of welders is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.029. Make a valid conclusion based on this p-value.

    Answers:

    • At the 5% level, the career analyst cannot conclude that the mean salary for welders did rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for welders did rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst can conclude that the mean salary for welders did not rise from the current mean.

  • 17.

    A school district believes that the mean number of students who ride the bus to school each year has risen from the current mean of 370 students. To test their hypothesis, a simple random sample of students is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.421. Based on this p-value, what conclusion can be made?

    Answers:

    • At the 5% level, the school district can conclude that the mean number of students who ride the bus each year did not rise from the current mean.

    • At the 5% level, the school district cannot conclude that the mean number of students who ride the bus each year did rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the school district can conclude that the mean number of students who ride the bus each year did rise from the current mean.

  • 18.

    A baseball coach believes that the mean number of home runs his team hits in a season has risen from the current mean of 34 home runs. To test the hypothesis, a simple random sample of baseball seasons is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.044. What conclusion can be made based on this p-value?

    Answers:

    • At the 10% level, the coach cannot conclude that the mean number of home runs hit in a season increased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of home runs hit in a season increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach can conclude that the mean number of home runs hit in a season decreased from the current mean.

  • 19.

    A sandwich shop believes that the mean number of sandwiches sold per day has risen from the current mean of 150 sandwiches. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.102. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • At the 10% level, the sandwich shop cannot conclude that the mean number of sandwiches sold per day increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the sandwich shop can conclude that the mean number of sandwiches sold per day decreased from the current mean.

    • At the 10% level, the sandwich shop can conclude that the mean number of sandwiches sold per day increased from the current mean.

  • 20.

    A farmer believes that since he started using a new type of fertilizer, the mean number of bushels of wheat he harvests per season has risen from the current mean of 200 bushels. To test the hypothesis, a simple random sample of growing seasons is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.031. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • At the 3% level, the farmer can conclude that the mean number of bushels harvested per season decreased from the current mean.

    • At the 3% level, the farmer cannot conclude that the mean number of bushels harvested per season increased from the current mean.

    • At the 3% level, the farmer can conclude that the mean number of bushels harvested per season increased from the current mean.

    • No conclusion can be made based on the given p-value.

  • 21.

    A career analyst believes that the mean salary for doctors has risen from the current mean of $97,000. To test their hypothesis, a simple random sample of doctors is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.003. Make a valid conclusion based on this p-value.

    Answers:

    • At the 5% level, the career analyst can conclude that the mean salary for doctors did rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst cannot conclude that the mean salary for doctors did rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for doctors did not rise from the current mean.

  • 22.

    A college believes that the mean number of students who enroll each year has declined from the current mean of 1500 students. To test their hypothesis, a simple random sample of years is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.068. Based on this p-value, what conclusion can be made?

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the college can conclude that the mean number of students who enroll each year did rise from the current mean.

    • At the 5% level, the college cannot conclude that the mean number of students who enroll each year did rise from the current mean.

    • At the 5% level, the college can conclude that the mean number of students who enroll each year did not rise from the current mean.

  • 23.

    A hockey coach believes that the mean number of goals his team scores in a game has risen from the current mean of 1 goal. To test the hypothesis, a simple random sample of games is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.095. What conclusion can be made based on this p-value?

    Answers:

    • At the 10% level, the coach can conclude that the mean number of goals scored in a game decreased from the current mean.

    • At the 10% level, the coach cannot conclude that the mean number of goals scored in a game increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach can conclude that the mean number of goals scored in a game increased from the current mean.

  • 24.

    A flower shop believes that the mean number of flowers sold per day has risen from the current mean of 75 flowers. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.209. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • At the 10% level, the flower shop can conclude that the mean number of flowers sold per day increased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the flower shop can conclude that the mean number of flowers sold per day decreased from the current mean.

    • At the 10% level, the flower shop cannot conclude that the mean number of flowers sold per day increased from the current mean.

  • 25.

    A carpenter believes that since he started using a new tool, the mean number of minutes it takes him to complete a wood project has declined from the current mean of 120 minutes. To test the hypothesis, a simple random sample of wood projects is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.027. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 3% level, the carpenter cannot conclude that the mean number of minutes it takes to complete a wood project decreased from the current mean.

    • At the 3% level, the carpenter can conclude that the mean number of minutes it takes to complete a wood project decreased from the current mean.

    • At the 3% level, the carpenter can conclude that the mean number of minutes it takes to complete a wood project increased from the current mean.

  • 26.

    A career analyst believes that the mean salary for engineers has risen from the current mean of $81,000. To test their hypothesis, a simple random sample of engineers is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.047. Make a valid conclusion based on this p-value.

    Answers:

    • At the 5% level, the career analyst can conclude that the mean salary for engineers did rise from the current mean.

    • At the 5% level, the career analyst can conclude that the mean salary for engineers did not rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the career analyst cannot conclude that the mean salary for engineers did rise from the current mean.

  • 27.

    A university believes that the mean number of students who enroll with an undeclared major each year has risen from the current mean of 230 students. To test their hypothesis, a simple random sample of students is taken and a significance test is performed at the 5% level. The results generate a p-value of 0.077. Based on this p-value, what conclusion can be made?

    Answers:

    • At the 5% level, the university can conclude that the mean number of students who enroll with an undeclared major each year did not rise from the current mean.

    • At the 5% level, the university can conclude that the mean number of students who enroll with an undeclared major each year did rise from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 5% level, the university cannot conclude that the mean number of students who enroll with an undeclared major each year did rise from the current mean.

  • 28.

    A track and field coach believes that the mean number of athletes on the team each season has risen from the current mean of 60 athletes. To test the hypothesis, a simple random sample of track and field seasons is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.143. What conclusion can be made based on this p-value?

    Answers:

    • No conclusion can be made based on the given p-value.

    • At the 10% level, the coach cannot conclude that the mean number of athletes on the team each season increased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of athletes on the team each season decreased from the current mean.

    • At the 10% level, the coach can conclude that the mean number of athletes on the team each season increased from the current mean.

  • 29.

    A grocery store believes that the mean number of plastic bags used per day has risen from the current mean of 1200 bags. To test their hypothesis, a simple random sample of days is taken and a significance test is performed at the 10% level. The results generate a p-value of 0.199. Given this p-value, make a valid conclusion for this scenario.

    Answers:

    • At the 10% level, the grocery store can conclude that the mean number of plastic bags used per day decreased from the current mean.

    • At the 10% level, the grocery store can conclude that the mean number of plastic bags used per day increased from the current mean.

    • At the 10% level, the grocery store cannot conclude that the mean number of plastic bags used per day increased from the current mean.

    • No conclusion can be made based on the given p-value.

  • 30.

    A movie theater believes that the mean number of popcorn bags sold per movie showing has risen from the current mean of 30 bags of popcorn. To test the hypothesis, a simple random sample of movie showings is taken and a significance test is performed at the 3% level. The results generate a p-value of 0.309. For this scenario, make a valid conclusion based on the generated p-value.

    Answers:

    • At the 3% level, the movie theater can conclude that the mean number of popcorn bags sold per movie showing decreased from the current mean.

    • No conclusion can be made based on the given p-value.

    • At the 3% level, the movie theater cannot conclude that the mean number of popcorn bags sold per movie showing increased from the current mean.

    • At the 3% level, the movie theater can conclude that the mean number of popcorn bags sold per movie showing increased from the current mean.

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