Questions: students are shown below. selected female statistics Female: 95 Assume both follow a Normal distribution. What can be concluded the the α=0.10 level of significance level of significance? For this study, we should use t-test for the difference between two independent population means a. The null and alternative hypotheses would be: H0 : μ1 > μ2 H1 : μ1 ≠ μ2 b. The test statistic = -0.989 (please show your answer to 3 decimal places.) c. The p-value = 0.3367 (Please show your answer to 4 decimal places.)

students are shown below.
selected female statistics

Female: 95
Assume both follow a Normal distribution. What can be concluded the the α=0.10 level of significance level of significance?

For this study, we should use t-test for the difference between two independent population means
a. The null and alternative hypotheses would be:
H0 : μ1 > μ2
H1 : μ1 ≠ μ2
b. The test statistic = -0.989 (please show your answer to 3 decimal places.)
c. The p-value = 0.3367 (Please show your answer to 4 decimal places.)

Transcript text: students are shown below. selected female statistics Female: 95 Assume both follow a Normal distribution. What can be concluded the the $\alpha=0.10$ level of significance level of significance? For this study, we should use $t$-test for the difference between two independent population means a. The null and alternative hypotheses would be: $H_{0}$ : $\mu 1$ $\square$ $>$ $\mu 2$ $\square$ $\square$ 0 $H_{1}$ : $\mu 1$ ‡ $\mu 2$ $\square$ (Please enter a decimal) $\square$ $\infty$ 0 b. The test statistic $\square$ $\square$ $-0.989$ (please show your answer to 3 decimal places.) $\square$ c. The $p$-value $=$ $\square$ 0.3367 (Please show your answer to 4 decimal places.)

Solution

Solution Steps

Step 1: Hypotheses

We set up the null and alternative hypotheses as follows: $H_0: \mu_1 = \mu_2$ $H_1: \mu_1 \neq \mu_2$

Step 2: Standard Error Calculation

The standard error $SE$ is calculated using the formula: $SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{10.0}{5} + \frac{10.0}{5}} = 2.0$

Step 3: Test Statistic Calculation

The test statistic $t$ is computed as: $t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{96.0 - 92.0}{2.0} = 2.0$

Step 4: Degrees of Freedom Calculation

The degrees of freedom $df$ are calculated using the formula: $df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{16.0}{2.0} = 8.0$

Step 5: P-value Calculation

The p-value $P$ is calculated as: $P = 2(1 - T(|t|)) = 2(1 - T(2.0)) = 0.0805$

Final Answer

a. The null and alternative hypotheses are: $H_0: \mu_1 = \mu_2, \quad H_1: \mu_1 \neq \mu_2$
b. The test statistic is: $t = 2.0$
c. The p-value is: $P = 0.0805$