PLease include 4 Decimal places!! ### Comparison of Female versus Male Class AttendanceWe are interested in comparing female versus male class attendance. The following data is provided:| Gender | Female | Male ||--------|--------|------|| **Sample Size** | 10 | 11 || **Average Attendance Percentage** | 88.5 | 86.75 || **Sample Standard Deviation** | 12.53 | 13.07 |#### Questions:a. What is the 99% confidence interval for the difference between the average attendance between female and male?b. What is the test statistic for the difference between female and male?c. What is the p-value?---This data will assist in understanding and carrying out a comparative analysis on class attendance across different gender groups. The sample sizes, averages, and standard deviations are key metrics used in calculating metrics such as confidence intervals, test statistics, and p-values.

a. The pooled estimator of σ2 is, sp2=n1-1s12+n2-1s22n1+n2-2=10-112.532+11-113.07210+11-2=164.2767…

Answered: а. What is the 99% confidence interval…

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PLease include 4 Decimal places!!

### Comparison of Female versus Male Class Attendance

We are interested in comparing female versus male class attendance. The following data is provided:

| Gender | Female | Male |
|--------|--------|------|
| **Sample Size** | 10 | 11 |
| **Average Attendance Percentage** | 88.5 | 86.75 |
| **Sample Standard Deviation** | 12.53 | 13.07 |

#### Questions:
a. What is the 99% confidence interval for the difference between the average attendance between female and male?

b. What is the test statistic for the difference between female and male?

c. What is the p-value?

---

This data will assist in understanding and carrying out a comparative analysis on class attendance across different gender groups. The sample sizes, averages, and standard deviations are key metrics used in calculating metrics such as confidence intervals, test statistics, and p-values.

Expert Solution

Step 1

The pooled estimator of $σ^{2}$ is,

$\begin{array}{rcl} s_{p}^{2} & = & \frac{(n_{1} - 1) s_{1}^{2} + (n_{2} - 1) s_{2}^{2}}{n_{1} + n_{2} - 2} \\ = & \frac{(10 - 1) 12 . 53^{2} + (11 - 1) 13 . 07^{2}}{10 + 11 - 2} \\ = & 164.2767 \end{array}$

Critical value:

The critical value of t-distribution at 19 degrees of freedom can be obtained using the excel formula “=T.INV.2T(0.01,19)”.

The critical value is 2.8609.

The 99% confidence interval for the difference between the average attendance between female and male is,

$\begin{array}{rcl} C I & = & ({\bar{x}}_{1} - {\bar{x}}_{2}) \pm t_{\frac{α}{2}} \sqrt{s_{p}^{2} (\frac{1}{n_{1}} + \frac{1}{n_{2}})} \\ = & (88.5 - 86.75) \pm 2.8609 \sqrt{164.2767 (\frac{1}{10} + \frac{1}{11})} \\ = & 1.75 \pm 16.0215 \\ = & (- 14.2715, 17.7715) \end{array}$

Thus, the 99% confidence interval for the difference between the average attendance between female and male is -14.2715 and 17.7715.

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