An evaluation was recently performed on brands and data werecollected that classified each brand as being in the technology orfinancial institutions sector and also reported the brand value.The results in terms of value​ (in millions of​ dollars) are shownin the accompanying data table. Complete parts​ (a) through​(c).

BRAND VALUES:

Technology: 281, 377, 491, 429, 406, 584, 641,624

Financial Institutions: 517, 832, 819, 804,937, 995, 1035, 1094

a.)

Assuming the population variances are​ equal, is there evidencethat the mean brand value is different for the technology sectorthan for the financial institutions​ sector? (Use α=0.05​.)

Determine the hypotheses. Let μ1 be the mean brand value for thetechnology sector and μ2 be the mean brand value for the financialinstitutions sector. Choose the correct answer below.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-Find the test statistic.

^tSTAT=___

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brandvalue for the technology sector is different from the mean brandvalue for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brandvalue for the technology sector is different from the mean brandvalue for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the meanbrand value for the technology sector is different from the meanbrand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the meanbrand value for the technology sector is different from the meanbrand value for the financial institutions sector.

b.)

-Repeat​ (a), assuming that the population variances are notequal.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-FInd the test statistic.

^tSTAT=____

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brandvalue for the technology sector is different from the mean brandvalue for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brandvalue for the technology sector is different from the mean brandvalue for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the meanbrand value for the technology sector is different from the meanbrand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the meanbrand value for the technology sector is different from the meanbrand value for the financial institutions sector.

c.)

-Compare the results of (a) and (b).

A. The conclusions for parts​ (a) and​ (b) are different. Rejectthe null hypothesis in​ (b) and do not reject it in​ (a).

B.The conclusions for parts​ (a) and​ (b) both reject the nullhypothesis.

C.The conclusions for parts​ (a) and​ (b) both do not reject thenull hypothesis.

D. The conclusions for parts​ (a) and​ (b) are different. Rejectthe null hypothesis in​ (a) and do not reject it in​ (b).