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12 December, 19:09

Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate?

A. About 95% of the heights of all students at the college will be contained in these interval

B. About 95% of the time, a student's sample mean height will be contained in his or her interval.

C. About 95% of the intervals will contain the population mean height.

D. About 95% of the intervals will be identical.

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  1. 12 December, 19:49
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    Correct option: (C)

    Step-by-step explanation:

    The (1 - α) % confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

    Or, the (1 - α) % confidence interval for the parameter implies that there is (1 - α) % confidence or certainty that the true parameter value is contained in the interval.

    Or, if n such (1 - α) % confidence intervals are constructed then (1 - α) % of these interval will consist of the true parameter value.

    It is provided that each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college.

    So there sill be n = 250, 95% confidence intervals for mean height of all students at the college.

    Then 95% of these 250 confidence intervals for mean will consist of the true mean height of the college students.

    Thus, the correct option is (C).
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