Question

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

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asked 2020-10-28
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

Answers (1)

2020-10-29
Step 1
Given:
Sample Size \(\displaystyle{\left({n}\right)}={49}\)
Sample Mean \(\displaystyle{\left(\overline{{X}}\right)}={72}\)
Population standard deviation \(\displaystyle{\left(\sigma\right)}={13.1}\)
Step 2
90% Confidence interval \(\displaystyle=\overline{{X}}\pm{Z}_{{\frac{\alpha}{{2}}}}{\left(\frac{\sigma}{\sqrt{{n}}}\right)}\)
\(\displaystyle={72}\pm{1.165}{\left(\frac{13.1}{\sqrt{{49}}}\right)}\)
\(\displaystyle={72}\pm{3.0785}\)
\(\displaystyle={\left({68.9215},{75.0785}\right)}\)
\(\displaystyle={\left({68.92},{75.08}\right)}\)
Since area corresponding to z value is given in z-table as:
\(\displaystyle{Z}_{{\frac{\alpha}{{2}}}}={Z}_{{\frac{0.10}{{2}}}}\)
\(\displaystyle={Z}_{{{0.05}}}\)
\(= 1.645\)
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