Test: Chapter 6 Exam Submit Test This Question: 1 pt 9 of 20 (0 complete) This T

Question

Test: Chapter 6 Exam Submit Test This Question: 1 pt 9 of 20 (0 complete) This Test: 20 pts possible Use the standard normal distribution or the t-distribution to construct a 99% 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 17 mortgage institutions, the mean interest rate was 3.45% and the standard deviation was 0.44%. 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 is known ( B. Use a normal distribution because the interest rates are normally distributed and is known ° C. Use a t-distribution because it is a random sample, is unknown, and the interest rates are normally distributed D. Use a normal distribution because n

Explanation / Answer

we must use a t distribution becuase

it is a random sample
population standard deviation is not known
and the sample size is less than 30

the correct choice is C

The CI is given as

mean +- t*sd/sqrt(n)

so 3.45 +- t*0.44/sqrt(17)

we see the t critical value as 2.921 for df = n -1 = 17-1 = 16 and alpha = 0.01

3.45 +- 2.921*0.44/sqrt(17), solving for plus and minus signs

3.13 and 3.76

so we can say that we are 99% confident that the true value of the mean would lie in this interval

Hence B

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