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Interpreting a Confidence Interval for a Population Proportion

  • 1.

    A person took a sample of 100 individuals and noted how many of them like coffee. A 99% confidence interval constructed with this sample proportion lies between 0.3 and 0.36. What does this statement interpret?

    Answers:

    • This indicates that we are 99% confident that the true population proportion is the middle value of the interval (0.3,0.36).

    • This indicates that we are 99% confident that the true population proportion is contained by the interval (0.3,0.36).

    • Cannot be determined.

    • This indicates that we are 99% confident that the true population proportion is true.

  • 2.

    Anna took a sample of 70 men in an area to survey the proportion who play golf. She formed an 80% confidence interval for the population proportion in the interval (0.42, 0.58). Which of the given options is the sample proportion?

    Answers:

    • 0.5

    • 0.6

    • 0.53

    • 0.43

  • 3.

    A manager surveyed a certain number of employees in his firm to know how many of them have been abroad. Interpret the 90% confidence interval of (0.12, 0.18).

    Answers:

    • This indicates that 90% of the samples will have a sample proportion contained by the interval (0.12, 0.18).

    • Cannot be determined

    • This indicates that 90% of the samples will have a sample proportion outside the interval (0.12, 0.18).

    • This indicates that 90% of the samples will have a sample proportion in the middle of the interval (0.12, 0.18).

  • 4.

    Liam took a crate with a certain number of red and blue balls and counted the number of red balls. An 85 % confidence interval created with this sample proportion lies between 0.77 and 0.83. Determine the proportion of the sample taken.

    Answers:

    • 0.7

    • 0.77

    • 0.83

    • 0.8

  • 5.

    A doctor investigated 60 babies in an area and recorded the proportion of babies with curly hair. She formed a 95% confidence interval for the population proportion in the interval (0.6, 0.7). Choose the correct interpretation of this confidence interval.

    Answers:

    • This indicates that we are 95% confident that the true population proportion is the middle value of the interval (0.6, 0.7).

    • This indicates that we are 95% confident that the true population proportion is outside the interval (0.6, 0.7).

    • This indicates that we are 95% confident that the true population proportion is contained by the interval (0.6, 0.7).

    • Cannot be determined

  • 6.

    Mr. Bill took a random sample of 55 students and noted the proportion of them liking chess. Calculate the sample proportion if the 75% confidence interval for the population proportion lies between 0.4 and 0.8.

    Answers:

    • 0.6

    • 0.7

    • 0.5

    • 0.8

  • 7.

    Peter randomly choose a certain number of milk pouches and noted the pouches made from soya. A 99% confidence interval constructed with this sample proportion lies between 0.19 and 0.31. What does this statement interpret?

    Answers:

    • This indicates that we are 99% confident that the true population proportion is the least value in the interval (0.19,0.31).

    • This indicates that we are 99% confident that the true population proportion is contained by the interval (0.19,0.31).

    • This indicates that we are 99% confident that the true population proportion is the middle value in the interval (0.19,0.31).

    • This indicates that we are 99% confident that the true population proportion is the maximum value in the interval (0.19,0.31).

  • 8.

    Revan chose a random sample of female workers in an organization and recorded the proportion with blonde hair. She formed an 80% confidence interval for the population proportion in the interval (0.13, 0.27). Which of the given choices is the sample proportion?

    Answers:

    • 0.25

    • 0.3

    • 0.15

    • 0.2

  • 9.

    A person took a sample of 100 workers and noted how many of them are above 35 years. Interpret the 75% confidence interval for the population proportion in the interval (0.23, 0.47).

    Answers:

    • 75% of the samples will have false results.

    • 75% of the samples will have the proportion contained by the interval (0.23, 0.47).

    • 75% of the samples will have true results.

    • 75% of the samples will have the proportion as the middle value of the interval (0.23, 0.47).

  • 10.

    Mrs. Smith took a random sample of students in her school and recorded the proportion of students who scored more than 80% in the last mathematics examination. A 95% confidence interval created with this sample proportion lies between 0.05 and 0.15. Identify the proportion of the sample taken.

    Answers:

    • 0.3

    • 0.2

    • 0.4

    • 0.1

  • 11.

    Sarah took a sample of 70 women in an area to survey the proportion who like live music shows. She formed a 90% confidence interval for the population proportion in the interval (0.63, 0.73). Select the correct interpretation of this confidence interval.

    Answers:

    • This indicates that we are 90% confident that the true population proportion is contained by the interval (0.63, 0.73).

    • This indicates that we are 90% confident that the true population proportion is above the interval (0.63, 0.73).

    • This indicates that we are 90% confident that the true population proportion is the middle value of the interval (0.63, 0.73).

    • This indicates that we are 90% confident that the true population proportion is below the interval (0.63, 0.73).

  • 12.

    A person investigated 75 individuals in a city and noted the proportion with spectacles. Evaluate the sample proportion for a 95% confidence interval for the population proportion of the interval (0.25, 0.35).

    Answers:

    • 0.3

    • 0.36

    • 0.27

    • 0.33

  • 13.

    An employer surveyed a certain number of employees in his company to know how many of them are vaccinated for a particular disease. A 75% confidence interval constructed with this sample proportion lies between 0.15 and 0.35. Interpret this statement.

    Answers:

    • This indicates that 75% of the samples will have a sample proportion below the interval (0.15,0.35).

    • This indicates that 75% of the samples will have a sample proportion contained by the interval (0.15,0.35).

    • This indicates that 75% of the samples will have a sample proportion of the middle value of the interval (0.15,0.35).

    • This indicates that 75% of the samples will have a sample proportion above the interval (0.15,0.35).

  • 14.

    Noah took a bag with a certain number of white and black cards. He noted the number of white cards. He formed a 95% confidence interval for the population proportion in the interval (0.36, 0.44). Which of the following options is the sample proportion?

    Answers:

    • 0.44

    • 0.4

    • 0.3

    • 0.36

  • 15.

    Mr. Brown randomly chose some children from an area and asked them if they play online games. Interpret the 80% confidence interval for the population proportion between 0.27 and 0.33.

    Answers:

    • This indicates that we are 80% confident that the true population proportion is contained by the interval (0.27,0.33).

    • This indicates that we are 80% confident that the true population proportion is the least value of the interval (0.27,0.33).

    • This indicates that we are 80% confident that the true population proportion is the maximum value of the interval (0.27,0.33).

    • This indicates that we are 80% confident that the true population proportion is the middle value of the interval (0.27,0.33).

  • 16.

    A person took a sample of 100 individuals and noted how many of them prefer public transport to commute. A 75% confidence interval created with this sample proportion lies between 0.58 and 0.82. Determine the proportion of the sample taken.

    Answers:

    • 0.6

    • 0.5

    • 0.8

    • 0.7

  • 17.

    Oliver interviewed 65 voters and recorded the proportion who were happy with the bill recently passed. He formed an 85% confidence interval for the population proportion in the interval (0.23, 0.43). Choose an accurate interpretation of this confidence interval.

    Answers:

    • This indicates that we are 85% confident that the true population proportion is the least value of the interval (0.23, 0.43).

    • This indicates that we are 85% confident that the true population proportion is contained by the interval (0.23, 0.43).

    • This indicates that we are 85% confident that the true population proportion is the middle value of the interval (0.23, 0.43).

    • This indicates that we are 85% confident that the true population proportion is the maximum value of the interval (0.23, 0.43).

  • 18.

    Diana took a sample of 70 adults in an area to survey the proportion who have a regular job. Calculate the sample proportion if a 99% confidence interval lies between 0.21 and 0.29.

    Answers:

    • 0.24

    • 0.25

    • 0.23

    • 0.26

  • 19.

    Jina surveyed some students in a university and recorded the proportion of the students who were satisfied with the online tools. A 75% confidence interval constructed with this sample proportion lies between 0.63 and 0.67. What does this statement interpret?

    Answers:

    • Cannot be determined.

    • This indicates that 75% of the samples will have a sample proportion contained by the interval (0.63, 0.67).

    • This indicates that 75% of the samples will have a sample proportion not contained by the interval (0.63, 0.67).

    • This indicates that 75% of the samples will answer truly.

  • 20.

    A manager surveyed a certain number of female workers in his organization to know how many of them are mothers. She formed a 90% confidence interval for the population proportion in the interval (0.33, 0.37). Which of the following choices is the sample proportion?

    Answers:

    • 0.35

    • 0.31

    • Cannot be determined

    • 0.39

  • 21.

    Revan interviewed 45 employees of a company and recorded the proportion of employees who read the newspaper daily. Interpret the 80% confidence interval for the population proportion in the interval (0.09, 0.13).

    Answers:

    • This indicates that we are 80% confident that the true population proportion is above the interval (0.09, 0.13).

    • This indicates that we are 80% confident that the true population proportion is contained by the interval (0.09, 0.13).

    • Cannot be determined.

    • This indicates that we are 80% confident that the true population proportion is below the interval (0.09, 0.13).

  • 22.

    Daniel took a sample of 70 workers in an organization to survey the proportion who have a graduation degree. A 75% confidence interval created with this sample proportion lies between 0.32 and 0.48. Identify the proportion of the sample taken.

    Answers:

    • 0.6

    • 0.4

    • 0.2

    • 0.8

  • 23.

    Kevin took a sample of some residents in an area and noted the number of residents with a driving license. He formed an 80% confidence interval for the population proportion in the interval (0.75,0.85). Select an accurate interpretation of this confidence interval.

    Answers:

    • This indicates that we are 80% confident that the true population proportion is contained by the interval (0.75, 0.85).

    • This indicates that we are 80% confident that the true population proportion is above the interval (0.75, 0.85).

    • This indicates that we are 80% confident that the true population proportion is below the interval (0.75, 0.85).

    • This indicates that we are 80% confident that the true population proportion is the center of the interval (0.75, 0.85).

  • 24.

    William choose a certain number of pumpkins from his garden and noted the number of pumpkins weighing more than 20 pounds. Evaluate the sample proportion for a 99% confidence interval for the population proportion between 0.58 and 0.62.

    Answers:

    • 0.5

    • 0.7

    • 0.8

    • 0.6

  • 25.

    A person took a sample of 100 children and noted how many of them like chocolates. An 85% confidence interval constructed with this sample proportion lies between 0.36 and 0.54. What does this statement interpret?

    Answers:

    • This indicates that we are 85% confident that the true population proportion is the lowest value of the interval (0.36, 0.54).

    • This indicates that we are 85% confident that the true population proportion is the middle value of the interval (0.36, 0.54).

    • This indicates that we are 85% confident that the true population proportion is the highest value of the interval (0.36, 0.54).

    • This indicates that we are 85% confident that the true population proportion is contained by the interval (0.36, 0.54).

  • 26.

    Jack took a random sample of 85 fuses manufactured by a unit and noted the number of defective fuses. He formed an 80% confidence interval for the population proportion in the interval (0.11, 0.19). Which of the given options is the sample proportion?

    Answers:

    • 0.15

    • 0.17

    • 0.13

    • 0.19

  • 27.

    Liza took a sample of 70 bulbs manufactured in a factory to survey the proportion of defective bulbs. Interpret the 75% confidence interval for the population proportion in the interval (0.27, 0.53).

    Answers:

    • This indicates that 75% of the samples will have a sample proportion below the interval (0.27, 0.53).

    • Cannot be determined

    • This indicates that 75% of the samples will have a sample proportion contained by the interval (0.27, 0.53).

    • This indicates that 75% of the samples will have a sample proportion above the interval (0.27, 0.53).

  • 28.

    An HR surveyed a certain number of male workers in his company to know how many of them like football. A 90% confidence interval created with this sample proportion lies between 0.07 and 0.23. Determine the proportion of the sample taken.

    Answers:

    • 0.15

    • 0.19

    • 0.21

    • 0.11

  • 29.

    Mary randomly selected some plants in her garden and noted the number of plants with heights above 70 feet. She formed a 95% confidence interval for the population proportion in the interval (0.55, 0.6). Choose the correct interpretation of this confidence interval.

    Answers:

    • This indicates that we are 95% confident that the true population proportion is the center value of the interval (0.55, 0.6).

    • Cannot be determined.

    • This indicates that we are 95% confident that the true population proportion is outside the interval (0.55, 0.6).

    • This indicates that we are 95% confident that the true population proportion is contained by the interval (0.55, 0.6).

  • 30.

    A person took a sample of 100 women and noted how many of them are married. Calculate the sample proportion if the 99% confidence interval for the population proportion lies between 0.77 and 0.83.

    Answers:

    • 0.6

    • 0.2

    • 0.8

    • 0.4

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