You are given the sample mean and

Answered question

2022-04-27

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

Answer & Explanation

star233

star233

Skilled2022-05-14Added 403 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?