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An evaluation was recently performed on brands and data were collected that classified each brand as...

An evaluation was recently performed on brands and data were collected that classified each brand as being in the technology or financial institutions sector and also reported the brand value. The results in terms of value​ (in millions of​ dollars) are shown in 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 evidence that the mean brand value is different for the technology sector than for the financial institutions​ sector? (Use α=0.05​.)

Determine the hypotheses. Let μ1 be the mean brand value for the technology sector and μ2 be the mean brand value for the financial institutions 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 brand value for the technology sector is different from the mean brand value for the financial institutions sector.

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

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

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

b.)

-Repeat​ (a), assuming that the population variances are not equal.

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 brand value for the technology sector is different from the mean brand value for the financial institutions sector.

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

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

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

c.)

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

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

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

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

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

Solutions

Expert Solution

milcah answered 9 months ago
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