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Question 8 of 10 - Test 3
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Question 8 of 10
A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected a weight of the sample is
10.2g, and the standard deviation of weight among mice is
2g.
Find a 95% confidence interval for the mean weight of all the mice in the shipment.

10.2+-1.75

10.2+-1.11

10.2+-2.48

10.2+-2.30

A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected a weight of the sample is $10.2 \mathrm{~g}$ , and the standard deviation of weight among mice is $2 \mathrm{~g}$ . $\newline$ Find a $95\%$ confidence interval for the mean weight of all the mice in the shipment. $\newline$ $10.2 \pm 1.75$ $\newline$ $10.2 \pm 1.11$ $\newline$ $10.2 \pm 2.48$ $\newline$ $10.2 \pm 2.30$

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Interpret confidence intervals for population means

Full solution

Q. A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected a weight of the sample is

10.2 \mathrm{~g}

, and the standard deviation of weight among mice is

2 \mathrm{~g}

.

\newline

Find a

95\%

confidence interval for the mean weight of all the mice in the shipment.

\newline

10.2 \pm 1.75

\newline

10.2 \pm 1.11

\newline

10.2 \pm 2.48

\newline

10.2 \pm 2.30

Identify Mean and SD: Step $1$ : Identify the mean and standard deviation from the sample. Mean weight ( $\bar{x}$ ) = $10.2$ g, Standard deviation ( $s$ ) = $2$ g, Sample size ( $n$ ) = $5$ .
Calculate SEM: Step $2$ : Calculate the standard error of the mean (SEM). $\newline$ SEM = $\frac{s}{\sqrt{n}} = \frac{2}{\sqrt{5}} \approx 0.8944$ .
Determine t-value: Step $3$ : Determine the t-value for a $95$ % confidence interval with $n-1$ degrees of freedom. $\newline$ Using a t-distribution table for $4$ degrees of freedom at $95\%$ confidence, t-value $\approx 2.776$ .
Calculate Margin of Error: Step $4$ : Calculate the margin of error for the confidence interval. $\newline$ Margin of Error = $t$ -value $*$ SEM = \(2. $776$ $*$ $0$ . $8944$ \approx $2$ . $48$ \).
Construct Confidence Interval: Step $5$ : Construct the confidence interval. $\newline$ Confidence Interval = $\bar{x} \pm$ Margin of Error = $10.2 \pm 2.48$ .

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