A random sample of 45 home theater systems has a mean price of $139.00. Assume the population standard deviation is $15.70.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
EM
Re...
A random sample of 45 home theater systems has a mean price of $139.00. Assume the population standard deviation is $15.70.
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 ( ).
(Round to two decimal places as needed.)
Interpret the results. Choose the correct answer below.
O A. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price
lies in the second interval. The 95% confidence interval is wider than the 90%.
O B. 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%.
PDF
Professional
Ref.pdf
O C. 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 narrower than the 90%.
Click to select your answer(s).
Take a Test - Micha...
w
gSearch Textbook So.
DELL
Transcribed Image Text: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. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. EM Re... A random sample of 45 home theater systems has a mean price of $139.00. Assume the population standard deviation is $15.70. 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 ( ). (Round to two decimal places as needed.) Interpret the results. Choose the correct answer below. O A. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%. O B. 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%. PDF Professional Ref.pdf O C. 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 narrower than the 90%. Click to select your answer(s). Take a Test - Micha... w gSearch Textbook So. DELL
Expert Solution
Step 1 - Writing given data

Given that 

Random sample size (n) =45

Mean price (x¯)= $139

Population standard deviation (σ)=$15.70

We know that 

Confidence interval (CI)=x¯±Zcxσn

For 90% confidence (Zc ) =1.645

For 95% confidence (Zc) = 1.96

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