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?
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
since test is right tailed so
P-Value =P(Z>2.03) =0.0212
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
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