Question

# You are given the sample mean and the population standard deviation. Use this information to construct...

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.

A random sample of 60 home theater systems has a mean price of ​\$147.00. Assume the population standard deviation is ​\$19.40.

Construct a​ 90% confidence interval for the population mean. The​ 90% confidence interval is _____. ​(Round to two decimal places as​ needed.)

pt 2:

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.

From a random sample of 42 business​ days, the mean closing price of a certain stock was ​\$119.95. Assume the population standard deviation is ​\$9.93

The​ 90% confidence interval is ____. ​(Round to two decimal places as​ needed.)

pt 3:

Find the critical value (tc) for the confidence level c=0.9898 and sample size n=77.

tc=_____. ​(Round to the nearest thousandth as​ needed.)

Solution:

pt : 1 :- Given that n = 60, x = 147, σ = 19.40

90% Confidence level for Z = 1.645

95% Confidence level for Z = 1.96

=> 90% Confidence interval for the population = X +/- Z*σ/sqrt(n)
= 147 +/- 1.645*19.40/sqrt(60)
= (142.88 , 151.12)

=> 95% Confidence interval for the population = X +/- Z*σ/sqrt(n)
= 147 +/- 1.96*19.40/sqrt(60)
= (142.09 , 151.91)

pt 2 :- Given that n = 42, x = 119.95, σ = 9.93

=> 90% Confidence interval for the population = X +/- Z*σ/sqrt(n)
= 119.95 +/- 1.645*9.93/sqrt(42)
= (117.43 , 122.47)

=> 95% Confidence interval for the population = X +/- Z*σ/sqrt(n)
= 119.95 +/- 1.96*9.93/sqrt(42)
= (116.95 , 122.95)

pt 3 :- the confidence level c=0.98 and sample size n=7.

df = n-1 = 7-1 = 6

tc = 3.143

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