Question

#17

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Which interval is​ wider? If​ convenient, use technology to construct the confidence intervals.

A random sample of 34 gas grills has a mean price of ​$648.20

Assume the population standard deviation is ​$56.70

The​ 90% confidence interval is

​(______​,______).

Answer 1

Here we assume that the population standard deviation is ​$56.70

So we can use Z interval.

Let's use minitab

Step 1) Click on Stat>>>Basic Statistics >>1 sample Z...

Click on summarized data

Sample size = 34

Mean = 648.20

Standard deviation = 56.70

Step 2) then click on Option

Confidence level = 90.0

Alternative "not equal "

then click on OK

again click on OK

So we get the following output:

The assumed standard deviation = 56.7 N Mean SE Mean 34 648.20 9.72 (632.21, 664.19) 90% CI

From the above output the 90% confidence interval for population mean is  (632.21, 664.19)

The width of this interval = 664.19 - 632.21 = 31.98

Let's find 95% confidence interval for population mean.

Here we assume that the population standard deviation is ​$56.70

So we can use Z interval.

Let's use minitab

Step 1) Click on Stat>>>Basic Statistics >>1 sample Z...

Click on summarized data

Sample size = 34

Mean = 648.20

Standard deviation = 56.70

Step 2) then click on Option

Confidence level = 95.0

Alternative "not equal "

then click on OK

again click on OK

So we get the following output:

One-Sample Z The assumed standard deviation-56 .7 95% CI 34 648.20 9.72 (629.14, 667.26)

From the above output the 90% confidence interval for population mean is  (629.14, 667.26)

The width of this interval = 667.26 -629.14 = 38.12

95% confidence interval is wider than the 90% confidence interval.