For Questions 2, you should do the following: 1. State the null and alternative

Question

For Questions 2, you should do the following:

1. State the null and alternative hypotheses.

2. Decide whether you should use the z or the t distribution.

[Hint: Even though there is not a large difference in results using the z or the t distribution when the sample size is large, sample size should not be the basis for deciding whether the z or the t distribution should be used.]

3. Show your work for the calculation of the appropriate test statistic (z or t).

4. Find the p-value of the test statistic by using Excel.

[Hint: Be careful about whether you are looking for the area above or below the test statistic value - - that would be determined by the sign (> or <) in Ha. Be especially careful if the sign in Ha is .

5. State your statistical decision (reject Ho or do not reject Ho).

6. Did you find the evidence the problem was looking for?

[Hint: Be alert! For one or more of these problems you will have to revisit work that we studied earlier this term.]

Q2. First-year lawyers in a large city earn an average of $120,000 per year. A random sample of first-year lawyers at the Dewey, Cheatum, and Howe Law Firm (where first-year salaries are known to follow a normal distribution) reported the following salaries (in thousands of dollars):

160

155

110

120

135

185

110

110

135

140

150

145

180

100

115

112

Can we conclude that the mean salary of first-year lawyers at this firm is higher than the city average? (Use = .01)

Ho:                                Ha:

Should you be using z or t? (Explain.)

What is the value of the test statistic? (Show your work.)

What is the p-value? Find the p-value of the test statistic by using Excel.

Statistical decision:

Did you find the evidence the problem was looking for?

Explanation / Answer

1)Ho:mean=120000

Ha: mean>120000

2)here we will use t distribution as population std deviation is not known

3) t=2.325

4)p value =0.017

5)as p value is greater then 0.01 level we can not reject Ho

6)we do not have sufficient evidence to conclude that the mean salary of first-year lawyers at this firm is higher than the city average

X 160 155 110 120 135 185 110 110 135 140 150 145 180 100 115 112 mean(X) 135.125 std deviation(S) 26.018 std error =S/(n)1/2 6.504 t=(X-120)/std error 2.325 p value 0.017

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