Question

2. The following data were obtained in a su wine data were obtained in a study comparing persons with disabilities with persons without ies. A scale known as the Barriers to Health Promotion Activities for Disabled Persons (BHADP) Scale data. We believe that persons with disabilities score higher than persons without disabilities. Test the hypothesis at a 0.01 Disabled: -35.63 - 129 * = 6.85 Nondisabled: 28.85 ,- 132 5,= 4.46 a. State the null and alternative hypothesis. H : H : b. Specify the level of significance and identify the degrees of freedom if needed. df c. Sketch the sampling distribution, determine the critical value(s), and determine the rejection region(s). d. Find the standardized test statistic. 2. Make a decision to reject or fail to reject the null hypothesis Interpret the decision in the context of the original claim using a complete sentence. At the level of significance,

Answer 1

a)

Ho: μι 2 μ2 Ha: μι < μ2

b)

a = 0.01and df = 259.

c)

Based on the information provided, the significance level is a = 0.01, and the degrees of freedom are df = 259. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal: Hence, it is found that the critical value for this left-tailed test is te = -2.341, for a = 0.01 and df = 259. The rejection region for this left-tailed test is R = {tit < -2.341).

T-Test: t = 9.497, p = 1 6 8 10

d)

e)

since it is assumed that the population variances are equal, the t-statistic is computed as follows: X-X2 (nz-1) {t(n-1)3 ( +) 35.6322832-2 ) = 9.497 — (129-1)(132-1)4.462 (1+1)

f)

since it is observed that t = 9.497 > t = -2.341, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p=1, and since p=1 > 0.01, it is concluded that the null hypothesis is not rejected.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean ui is less than um, at the 0.01 significance level.