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 23 mortgage institutions, the mean interest rate was 3.59% and the standard deviation was 0.31%. Assume the interest rates are normally distributed Which distribution should be used to construct the confidence interval? A. Use a normal distribution because the interest rates are normally distributed and is known. B. Use a t-distribution because it is a random sample, is unknown, and the interest rates are normally distributed. ° C. Use a t-distribution because the interest rates are normally distributed and is known. 0 D. Use a normal distribution because n

Explanation / Answer

Solution:

n = 23, x = 3.59%, = 0.31%
A. Use a normal distribution because the interest rates are normally distributed and is known.
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95% confidence interval is:
CI = x ± Z/2 * (/n)
= 3.59 ± 1.96 *(0.31/23)
= 3.59 ± 0.1267
= (3.4633, 3.7167)
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B. with 99% confidence, it can be said that the population mean interest rate is between the bounds of the confidence interval.

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