Question

a physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. she randomly selected 55 men and 79 women to participate in the study. each subject was required to step up and down a 6 - inch platform. the pulse of each subject was then recorded. the following results were obtained
two sample t for men vs women
men n = 55, mean = 112.4, stdev = 11.8, se mean = 1.6
women n = 79, mean = 118.3, stdev = 14.4, se mean = 1.6
98% ci for mu men - mu women (-11.29, - 0.51)
t - test mu men = mu women (vs <)
t=-2.60 p = 0.0052 df = 128
(a) state the null and alternative hypotheses. which of the following is correct?
a. ( h_0:mu_1=mu_2;h_a:mu_1<mu_2 )
b. ( h_0:mu_1=mu_2;h_a:mu_1
eqmu_2 )
c. ( h_0:mu_1=mu_2;h_a:mu_1>mu_2 )
(b) identify the p - value and state the researchers conclusion if the level of significance was ( alpha = 0.02 ). what is the p - value?
p - value =

Explanation:

Step1: Identify the P - value from the given output

The output clearly states "T - Test mu Men = mu Women (vs < ) T = - 2.60 P = 0.0052 DF = 128". So, the P - value is directly given as \(P = 0.0052\).

Step2: Make a conclusion based on the significance level

We are given \(\alpha=0.02\). The decision rule for a hypothesis test is: if \(P - value<\alpha\), we reject the null hypothesis \(H_0\).
Since \(0.0052<0.02\) (i.e., \(P - value <\alpha\)), we reject the null hypothesis \(H_0:\mu_1 = \mu_2\).

Answer:

The P - value is \(0.0052\). Since \(P - value=0.0052<\alpha = 0.02\), the researcher rejects the null hypothesis. There is sufficient evidence at the \(\alpha = 0.02\) level of significance to conclude that the mean step - pulse of men is less than the mean step - pulse of women.