Question

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).

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

-Find the test statistic

-Find the p-Value

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

c. Compare the results of​ (a) and​ (b).

Technology	Financial Institutions
255	577
359	836
417	806
476	889
492	998
564	976
634	1022
631	1074

Answer 1

	Technology ( X )		Financial Institutions ( Y )
	255	49952.25	577	102560.0625
	359	14280.25	836	3751.5625
	417	3782.25	806	8326.5625
	476	6.25	889	68.0625
	492	182.25	998	10150.5625
	564	7310.25	976	6201.5625
	634	24180.25	1022	15562.5625
	631	23256.25	1074	31240.5625
Total	3828	122950	7178	177861.5

To Test :-

H0 :-  

H1 :-  

Test Statistic :-





t = -5.7135

Test Criteria :-
Reject null hypothesis if   


Result :- Reject Null Hypothesis

P value = 0.0000536

Decision based on P value

Reject null hypothesis if P value < α=0.05 level of significance

0.0000536 < 0.05, we reject null hypothesis

Conclusion :- Accept Alternative Hypothesis

There is sufficient evidence to support  the claim that the mean brand value is different for the technology sector than for the financial institutions​ sector.

Population variances are not equal.

Test Statistic :-


t = -5.7135

Test Criteria :-
Reject null hypothesis if   


DF = 13


Result :- Reject Null Hypothesis

P value = 0.00007131

Decision based on P value

Reject null hypothesis if P value < α=0.05 level of significance

0.00007131 < 0.05, we reject null hypothesis

Conclusion :- Accept Alternative Hypothesis

There is sufficient evidence to support  the claim that the mean brand value is different for the technology sector than for the financial institutions​ sector.

Part c)

In both the method we are reject the null hypothesis.