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 12 mortgage institutions, the mean interest rate was 3.67% and the standard deviation was 0.38%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a t-distribution because the interest rates are normally distributed and sigma is known. B. Use a t-distribution because it is a random sample, sigma is unknown, and the interest rates are normally distributed. C. Use a normal distribution because the interest rates are normally distributed and sigma is known. D. Use a normal distribution because n

Explanation / Answer

Solution:-

If is not known, then using t-distribution is correct. If is known, then using the normal distribution is correct.

(C) Use a normal distribution because the interest rates are normally distributed and sigma is known.

95% confidence interval - (0.0345 to 0.03890)

The Confidence Interval formula is

Where:

Sample Size: 12
Sample Mean: 0.0367
Sample Standard Deviation: 0.0038
Confidence Level: 95%

95% Confidence Interval: 0.0367 ± 0.0022

(0.0345 to 0.03890)

Interpret results - (B)

X ± Z s (n)

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