Questions: If your claim is in the alternative hypothesis and you reject the null hypothesis, then your conclusion would be: There is not sufficient evidence to warrant rejection of the original claim There is sufficient evidence to warrant rejection of the original claim There is not sufficient sample evidence to support the original claim The sample data support the original claim

Solution Steps

The Standard Error \( (SE) \) is calculated using the formula:

\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{0.133}{5} + \frac{0.157}{5}} = 0.2408 \]

The test statistic \( (t) \) is computed as follows:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{2.76 - 2.62}{0.2408} = 0.5813 \]

The degrees of freedom \( (df) \) are calculated using the formula:

\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{0.0034}{0.0004} = 7.9456 \]

The p-value \( (P) \) is determined using the formula:

\[ P = 2(1 - T(|t|)) = 2(1 - T(0.5813)) = 0.5771 \]

Given the significance level \( \alpha = 0.05 \):

• Since \( P = 0.5771 > 0.05 \), we do not reject the null hypothesis.

There is not sufficient evidence to warrant rejection of the original claim.

Final Answer