Questions: Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths ( mm ) of skulls from 150 A.D. Construct a 99% confidence interval estimate of the mean skull width. mm < µ < mm (Round to two decimal places as needed.)

Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths ( mm ) of skulls from 150 A.D. Construct a 99% confidence interval estimate of the mean skull width.
mm < µ < mm
(Round to two decimal places as needed.)

Transcript text: Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths ( mm ) of skulls from 150 A.D. Construct a $99 \%$ confidence interval estimate of the mean skull width. $\mathrm{mm}<\mu<\mathrm{mm}$ (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the Sample Mean ($\bar{X}$)

The sample mean ($\bar{X}$) is calculated as the average of the sample data: $\bar{X} = nan$.

Step 2: Calculate the Sample Standard Deviation ($s$)

The sample standard deviation ($s$) is calculated as: $s = nan$.

Step 3: Determine the Critical Value ($t^*$)

Based on the confidence level ($1 - \alpha = 0.99$) and degrees of freedom ($n-1 = -1$), the critical value ($t^_$) from the t-distribution is: $t^_ = nan$.

Step 4: Calculate the Margin of Error ($E$)

The margin of error ($E$) is calculated using the formula: $E = t^* \times \frac{s}{\sqrt{n}} = nan$.

Step 5: Construct the Confidence Interval

The confidence interval for the mean is given by $\bar{X} \pm E$, which is: (nan, nan).