# You measure the weight of 49 dogs , and find they have a mean weight of 72 ounces. Let's say the population standard deviation is 13.1 ounces. Based on this, construct a displaystyle{90}% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places

You measure the weight of 49 dogs , and find they have a mean weight of 72 ounces. Let's say the population standard deviation is 13.1 ounces. Based on this, construct a $90\mathrm{%}$ confidence interval for the true population mean dog weight.
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Aniqa O'Neill
Step 1
Given:
Sample Size $\left(n\right)=49$
Sample Mean $\left(\stackrel{―}{X}\right)=72$
Population standard deviation $\left(\sigma \right)=13.1$
Step 2
90% Confidence interval $=\stackrel{―}{X}±{Z}_{\frac{\alpha }{2}}\left(\frac{\sigma }{\sqrt{n}}\right)$
$=72±1.165\left(\frac{13.1}{\sqrt{49}}\right)$
$=72±3.0785$
$=\left(68.9215,75.0785\right)$
$=\left(68.92,75.08\right)$
Since area corresponding to z value is given in z-table as:
${Z}_{\frac{\alpha }{2}}={Z}_{\frac{0.10}{2}}$
$={Z}_{0.05}$
$=1.645$
Jeffrey Jordon