Question

Consider the following hypothesis test. H0: 1 - 2 ≤ 0 Ha: 1 - 2 > 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 40 n2 = 50 x1 = 25.2 x2 = 22.8 σ1 = 5.2 σ2 = 6.0 a. What is the value of the test statistic (round to 2 decimals)? b. What is the p-value (round to 4 decimals)? Use z-table. c. With = .05, what is your hypothesis testing conclusion?

Answer 1

we have to test that

we have for sample 1

sample size =n1=40 sample mean =m1=25.2 SD1=5.2

for sample 2

sample size =n2=50 sample mean =m2=22.8 SD2=6

a) test statistics is given by

b)

since test is right tailed so

P-Value =P(Z>2.03) =0.0212

c)

since P Value is less than level of significance hence we reject the null hypothesis that is there is enough evidence to conclude that population mean difference is more than ZERO