This Quiz: 10 pts poss You are given the sample mean and the population standard

Question

This Quiz: 10 pts poss You are given the sample mean and the population standard t Interpret the results and compare the widths of the confidence intervals If convenient, use technology to construct the d deviation Use this information to construct the 90% and 95% confidence ntevals for the confidonce intervals A random sample of 50 home theater systems has a mean price of $124.00 Assume the population standard deviation s $19 80 Construct a 90% confidence interval for the population mean The 90% confidence interval is (Round to two decimal places as needed.) construct a 95% confidence interval for the population mean The 95% confidence interval is D (Round to two decimal places as needed) >I Interpret the results Choose the correct answer below en opteinn with 90% confidence, it can be sad that the population mean proe ies rne fast nerval with 95% cot the second interval. The 95% confidence interval is wider than the 90% ce, gan besadharnepop ati A val wn 9% cot it can be sade att popul m np nk tin B. with 9 % confidence, t can be said that the populaton mean pro les n the the second interval The 95% confidence interval is narrower than the 90% with 90% confidence it can be said thatthe sample mean price les n thi str second interval The 95% confidence interval is wider than the 90% oc. Click to select your answer(s). arch

Explanation / Answer

Solution:- Given that n = 50, mean = $124.00 , sd = $19.80

a) 90% confidence interval for Z = 1.645

The 90% confidence interval is = X-bar ± Z * s/sqrt(n)
= 124.00 ± 1.645 * (19.80/sqrt(50))
= (119.39 , 128.61)

b) 95% confidence interval for Z = 1.96

The 95% confidence interval is = X-bar ± Z * s/sqrt(n)
= 124.00 ± 1.96 * (19.80/sqrt(50))
= (118.51 , 129.49)

=> option A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

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