Use the standard normal distribution or the t-distribution to construct a 95% co

Question

Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 46 people, the mean body mass index (BMI) was 28.5 and the standard deviation was 6.17. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a normal distribution because the sample is random, n greaterthanorequalto 30, and sigma is known. B. Use a t-distribution because the sample is random, n greaterthanorequalto 30, and sigma is unknown. C. Use a normal distribution because the sample is random, the population is normal, and sigma is known. D Use a t-distribution because the sample is random, the population is normal, and sigma is unknown. E Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n

Explanation / Answer

as sigma (i.e. standard deviation) of population is unknown, here we use t-distribution.

For 95% CI, t-value for 45 degrees of freedom is 2.021.

Here Margin of Error = 2.021 * 6.17/sqrt(46) = 1.8385

Lower limit = mean - ME = 28.5 - 1.8385 = 26.6615
Upper limit = mean + ME = 28.5 + 1.8385 = 30.3385

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