Question

use the following information to complete steps (a) through (d) below a random sample of size ( n_1 = 31 ) results in a sample mean of 124.3 and a sample standard deviation of 8.5. an independent sample of size ( n_2 = 50 ) results in a sample mean of 131.8 and sample standard deviation of 7.3. does this constitute sufficient evidence to conclude that the population means differ at the ( alpha = 0.10 ) level of significance? (c) use technology to calculate the p - value. 0.000 (round to three decimal places as needed.) (d) draw a conclusion based on the hypothesis test. choose the correct answer below. a. there is not sufficient evidence to reject the null hypothesis because the p - value ( <alpha ). b. there is sufficient evidence to reject the null hypothesis because the p - value ( <alpha ). c. there is sufficient evidence to reject the null hypothesis because the p - value ( >alpha ). d. there is not sufficient evidence to reject the null hypothesis because the p - value ( >alpha ).

Explanation:

Step1: Hypothesis testing rule

In hypothesis testing, if \(P - value<\alpha\), we reject the null hypothesis \(H_0\). Here, \(\alpha = 0.10\) and assume the \(P - value\) is calculated (from part (c) as a very small value, say \(P - value\approx0\)).

Step2: Conclusion based on rule

Since \(P - value\approx0<0.10=\alpha\), we reject the null hypothesis.

Answer:

B. There is sufficient evidence to reject the null hypothesis because the \(P -\)value \(<\alpha\)