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 3.57​% and the standard deviation was 0.38​%. Assume the interest rates are normally distributed.

Answer 1

Solution :

t _/2,df =

Margin of error = E = t_/2,df * (s /n)

= 2.201 * (0.0038 / 12)

Margin of error = E = 0.0024 = 0.24%

The 95% confidence interval estimate of the population mean is,

- E < < + E

3.57% - 0.24% < < 3.57% + 0.24%

3.33% < < 3.81%

(3.33% , 3.81%)