Consider the following hypothesis test. H0:μ1−μ2=0 Ha:μ1−μ2≠0The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1=80n2=70 x¯¯¯1=104x¯¯¯2=106 σ1=8.4σ2=7.6a. What is the value of the test statistic?b. What is the p-value?c. With α=.05,α=.05, what is your hypothesis testing conclusion?

a)  

b)

c) Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance

Step-by-step explanation:

Information given

represent the mean for 1

represent the mean for 2

represent the population standard deviation for 1

represent the population standard deviation for 2

sample size for the group 1

sample size for the group 2

z would represent the statistic

Hypothesis to test

We want to check if the two means for this case are equal or not, the system of hypothesis would be:

H0:

H1:

The statistic would be given by:

(1)

Part a

Replacing we got:

Part b

The p value would be given by this probability:

Part c

Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance