# You are given the sample mean and

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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Given:

Formula:

$=\overline{)x}±{z}_{\frac{\alpha }{2}}*\left\{\frac{\sigma }{\sqrt{n}}\right\}$

for $90%$ confidencr interval, ${z}_{\frac{\alpha }{2}}=1.645$

$=86.78±1.645*\left\{\frac{14.80}{\sqrt{69}}\right\}$

$=86.78±2.9$

for $95%$ confidencr interval, ${z}_{\frac{\alpha }{2}}=1.96$

$=86.78±1.96*\left\{\frac{14.80}{\sqrt{69}}\right\}$

$=86.78±3.5$

Which interval is​ wider?

The $95%$ confidence interval