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Quiz: Week7 CQulz This Question: 3 pts 130119 (6 complete) This Quiz: 60 pts pos

ID: 3330953 • Letter: Q

Question

Quiz: Week7 CQulz This Question: 3 pts 130119 (6 complete) This Quiz: 60 pts poss You are on the sample m an and the populat on standard deva on Use Ens nt mmation to construct the 0% and 9 % cor de ce n rvals l r the population mean which nt real is wider? If convenient, use iechnology to construct the confidence intervals A random sample of 46 gas grills has a mean price ot $649 90 Assume the population standard deviation is $55 60 The 90% confidence interval is OD (Round to one decimal place as needed ) The 95% confidence nterval is OD (Round to one decimal place as needed) Which interval is wider? Choose the correct answer below The 90% confidence interval The 95% confidence interval

Explanation / Answer

The formula for estimation is:

= M ± Z(sM)

where:

M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)

Calculation for 90%

M = 649.9
t = 1.64
sM = (55.62/46) = 8.2

= M ± Z(sM)
= 649.9 ± 1.64*8.2
= 649.9 ± 13.484

M = 649.9, 90% CI [636.416, 663.384].

You can be 90% confident that the population mean () falls between 636.416 and 663.384.

Calculation for 95%

M = 649.9
t = 1.96
sM = (55.62/46) = 8.2

= M ± Z(sM)
= 649.9 ± 1.96*8.2
= 649.9 ± 16.067

M = 649.9, 95% CI [633.833, 665.967].

You can be 95% confident that the population mean () falls between 633.833 and 665.967.

Therefore, 95% CI is wider.