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?

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

[tex]\bar X_{1}= 104[/tex] represent the mean for 1

[tex]\bar X_{2}= 106[/tex] represent the mean for 2

[tex]\sigma_{1}= 8.4[/tex] represent the population standard deviation for 1

[tex]\sigma_{2}= 7.6[/tex] represent the population standard deviation for 2

[tex]n_{1}=80[/tex] sample size for the group 1

[tex]n_{2}=70[/tex] 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:[tex]\mu_{1}=\mu_{2}[/tex]

H1:[tex]\mu_{1} \neq \mu_{2}[/tex]

The statistic would be given by:

[tex]z =\frac{\bar X_1-\bar X_2}{\sqrt{\frac{\sigma^2_1^2}{n_1} +\frac{\sigma^2_2^2}{n_2}}}= [/tex](1)

Part a

Replacing we got:

[tex]z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53[/tex]

Part b

The p value would be given by this probability:

[tex]p_v =2*P(z<-1.53)=0.126[/tex]

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