Question

Subjects in a study by Dabonneville et al. (A-9) included a sample of 40 men who claimed to engage in a variety of sports activities (multisport). The mean body mass index (BMI) for these men was 22.41 with a standard deviation of 1.27. A sample of 24 male rugby players had a mean BMI of 27.75 with a standard deviation of 2.64. Is there sufficient evidence for one to claim that, in general, rugby players have a higher BMI than the multisport men? Let a ¼ :01.

Answer 1

Answer:

The responses can be defined as follows:

Step-by-step explanation:

Given:

$H_o : \mu_1 = \mu_2\\\\H_a : \mu_1 < \mu_2$

Testing the hypothesis:

$Z=\frac{( \bar{x_1}-\bar{x_2})}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}$

   $=\frac{(22.41-27.75)}{\sqrt{(\frac{1.27^2}{40}+\frac{2.64^2}{24})}}\\\\=-9.29$

$a=0.01$

critical value $Z(0.01)=-2.33$ (using the standard normal table)

$Z=-9.29$ so, we reject $H_o$.