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A study measuring fitness level in teens randomly sampled 112 male teens and 101 female teens with a higher score indicating more fitness. Researchers suspected that the fitness level for male teens (μ1) is higher than for female teens (μ2), and wanted to check whether the data would supported this hypothesis.The following hypotheses were tested:H0: µ1 = µ2Ha: µ1 > µ2Sample N Mean SD1(M) 112 7.38 6.952(F) 102 7.15 6.31t-test of difference: df = 210 t-value = 0.25 p-value = 0.400Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that female and male teens do not differ in mean fitness score. The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens. The data provide sufficient evidence to reject H0 and to conclude that the mean fitness score for male teens is higher than that of female teens.

Question

A study measuring fitness level in teens randomly sampled 112 male teens and 101 female teens with a higher score indicating more fitness. Researchers suspected that the fitness level for male teens (μ1) is higher than for female teens (μ2), and wanted to check whether the data would supported this hypothesis.The following hypotheses were tested:H0: µ1 = µ2Ha: µ1 > µ2Sample N Mean SD1(M) 112 7.38 6.952(F) 102 7.15 6.31t-test of difference: df = 210 t-value = 0.25 p-value = 0.400Which of the following is an appropriate conclusion based on the output? The data provide sufficient evidence to conclude that male and female teens do not differ in mean fitness score. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that female and male teens do not differ in mean fitness score. The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens. The data provide sufficient evidence to reject H0 and to conclude that the mean fitness score for male teens is higher than that of female teens.

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Solution

The correct conclusion based on the output is: "The data do not provide sufficient evidence to conclude that the mean fitness score of male teens is higher than that of female teens."

Here's why:

The null hypothesis (H0) is that the mean fitness score of male teens (µ1) is equal to the mean fitness score of female teens (µ2). The alternative hypothesis (Ha) is that the mean fitness score of male teens is greater than that of female teens.

The t-test result gives a p-value of 0.400. This is greater than the commonly used significance level of 0.05. Therefore, we do not have enough evidence to reject the null hypothesis.

In other words, based on this sample, we cannot conclude that the mean fitness score of male teens is higher than that of female teens.

This problem has been solved

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