You are given the sample mean and

2022-04-27 Answered

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 69 ​dates, the mean record high daily temperature in a certain city has a mean of 86.78°F. Assume the population standard deviation is

14.80°F.

 

The​ 90% confidence interval is

 

The​ 95% confidence interval is

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Answers (1)

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Answered 2022-05-14 Author has 137 answers

Given: x=86.78, σ=14.80, n=69

Formula: Confidence interval for the population mean, μ

=x±zα2*{σn}

for 90% confidencr interval, zα2=1.645

=86.78±1.645*{14.8069}

=86.78±2.9

=(83.88, 89.68)

for 95% confidencr interval, zα2=1.96

=86.78±1.96*{14.8069}

=86.78±3.5

=(83.28, 90.82)

Which interval is​ wider?

The 95% confidence interval

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