The dataset below represents a sample of text messages sent during math class in a week by middle school students.

$\backslash$table$[[100,98,69,54,82,80,82,52,71,94,51]]$

Round your answers to three decimals where appropriate unless stated otherwise.

Calculate the sample mean and the sample standard deviation of the sample.

Sample Mean, $x$ :

Sample Standard Deviation, $s$ :

From the original sample data, take a bootstrap sample and record the values below.

Calculate the mean of your bootstrap sample.

Bootstrap sample mean $=||$

Instead of resampling manually as above, we'll use StatKey to automate the process for us$.$

Enter the data in Statkey first and generate a bootstrap distribution of about $10,000$ bootstrap samples. Use the distribution to construct a $99\%$ confidence interval to estimate the average number of texts sent during math class in a week by middle school students, Give results for both Percentile and Standard Error Plug$-$in methods.

After generating $10,000$ bootstrap samples, take a screenshot of your entire Statkey window and upload it below:

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Please upload the screenshot everytime you resubmit your work when attempting this question multiple times.

Percentile Method

Confidence Interval:

Plug$-$in Method

Bootstrap Standard Error, BSE:

$t-$critical value, $t_c$

Confidence Interval: