Question

In each of the following exercises, complete the ten-step
hypothesis testing procedure. State the assumptions that are
necessary for your procedure to be valid. For each exercise,
as

appropriate, explain why you chose a one-sided test or a two-sided
test. Discuss how you think researchers or clinicians might use the
results of your hypothesis test. What clinical or research
decisions or actions do you think would be appropriate in light of
the results of your test?

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 alpha=.01

Answer #1

Sample 1: rugby players. Sample 2: multisport

x_{1} = 27.75, x_{2} = 22.41, s_{1} =
2.64, s_{2} = 1.27, n_{1} = 24, n_{2} =
40

Alpha = 0.01, Degrees of freedom: df =
n_{1}+n_{2}-2 = 24+40-2 = 62

H_{0}: μ_{1}< μ_{2}, Rugby
players do not have a higher BMI than the multisport men

H_{1}: μ_{1} > μ_{2}, Rugby players
have a higher BMI than the multisport men

Test statistic: t = [(x_{1} -
x_{2})-(µ_{1}-µ_{2})] /
[((s_{1}^{2}(n_{1}-1) +
s_{2}^{2}(n_{2}-1))/(n_{1}+n_{2}-2))^0.5*(1/n_{1}+1/n_{2})^0.5]

= ((27.75-22.41)-0)/((((2.64*2.64*23)+(1.2*1.27*39))/(24+40-2))^0.5*(1/24+1/40)^0.5)

= 10.986

Critical value (Using Excel function ABS(T.INV(probability,df))) = ABS(T.INV(0.01,62)) = 2.388

Since test statistic is greater than critical value, we reject
the null hypothesis and conclude that μ_{1} >
μ_{2}.

So, rugby players have a higher BMI than the multisport men.

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