You are interested in examining the annual mean income for managers of banks and

Question

You are interested in examining the annual mean income for managers of banks and saving and loans institutions. You selected a random sample of eight of each kind of managers, and obtained the following results using Excel for the assumed 1% significance level:

t-Test: Two-Sample Assuming Unequal Variances

Sample1

Sample2

Banks

S&L

Mean

75935

     71482

Observations

8

8

Hypothesized Mean Difference

0

Df

13

t Stat

2.73

P(T<=t) one-tail

0.0086

t Critical one-tail

2.650

P(T<=t) two-tail

0.0172

t Critical two-tail

3.012

1. You want to prove that the average annual income of the managers of banks (1) is greater than the average annual income of the managers of savings and loans (2).

1 2                                

1 < 2                              

1 > 2                              

1 = 2

2. The null hypothesis is rejected if the value of the test statistics is?

3. The p-value of the test is?

4. At a 1% significance level, what is your conclusion?

t-Test: Two-Sample Assuming Unequal Variances

Sample1

Sample2

Banks

S&L

Mean

75935

     71482

Observations

8

8

Hypothesized Mean Difference

0

Df

13

t Stat

2.73

P(T<=t) one-tail

0.0086

t Critical one-tail

2.650

P(T<=t) two-tail

0.0172

t Critical two-tail

3.012

Explanation / Answer

1)1 > 2

2)

t Critical one-tail

2.650

3)p vlaue of this test =

P(T<=t) one-tail

0.0086

4) at 1 % , as p value is less then significance level, hence we reject null hypothesis. Hence we can conclude that verage annual income of the managers of banks (1) is greater than the average annual income of the managers of savings and loans

t Critical one-tail

2.650

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