A survey of 200 students provides a sample mean of 7.10 hours worked with a standard deviation of 5 hours. Suppose that this confidence interval was (6.82, 7.38). Which of these is a valid interpretation of this confidence interval?

A) There is a 95% probability that the true average number of hours worked by all UF students is between 6.82 and hours.

B) There is a 95% probability that a randomly selected student worked between 6.82 and 7.38 hours.

C) We are 95% confident that the average number of hours worked by students in our sample is between 6.82 and 7.38 hours.

D) We are 95% confident that the average number of hours worked by all UF students is between 6.82 and 7.38 hours.

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Mathematics

27 September, 16:10

A survey of 200 students provides a sample mean of 7.10 hours worked with a standard deviation of 5 hours. Suppose that this confidence interval was (6.82, 7.38). Which of these is a valid interpretation of this confidence interval?

A) There is a 95% probability that the true average number of hours worked by all UF students is between 6.82 and hours.

B) There is a 95% probability that a randomly selected student worked between 6.82 and 7.38 hours.

C) We are 95% confident that the average number of hours worked by students in our sample is between 6.82 and 7.38 hours.

D) We are 95% confident that the average number of hours worked by all UF students is between 6.82 and 7.38 hours.

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Answers (1)

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Moises Newman · Answer 1

Step-by-step explanation:

Confidence interval tells us the range of values within which the true mean lies. The narrower the confidence interval, the smaller the range of values. The wider the confidence interval, the larger the range of values.

Since the given confidence is given as (6.82, 7.38), then the valid interpretation of this confidence interval would be

C) We are 95% confident that the average number of hours worked by students in our sample is between 6.82 and 7.38 hours