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#### 1)Suppose the dean believes that the average salary of the population should be about \$58k per year, with a standard deviation of \$2k

###### Statistics

1)Suppose the dean believes that the average salary of the population should be about \$58k per year, with a standard deviation of \$2k. We need to conclude that the mean salary is less than what the dean has believed to be (30points, Review PPT Chapter 10). (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known)

1. What are the null and alternate hypotheses ?

1. What is the level of significance ?
2. What is the standard error ? 2000/(121^0.5) =
3. Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) ?

1. What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule .

1. Suppose the population standard deviation of \$2k (20points, Review PPT Chapter 9):  (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known)
1. What is the Z critical value of 95% confidence interval ?
2. What is the standard error ? 2000/(121^0.5) =
3. Please estimate the confidence interval of the population’s average salary (hint: write down the equation and calculate the results)

60,000 +/- 1.96(181.818)

60,000 +/- 356.36

1. Suppose the standard deviation of the collected data from 121 alumni is \$3k. Can we conclude that the true mean of alumni salary is different from \$58k (20 points; Review PPT Chapter 10)? (Hint: Hypothesis Testing and Confidence Interval - One sample; sample standard deviation is known)
1. What are the null and alternate hypotheses ?

1. Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic.

t = (60,000-58,000) / 3000/(121^0.5)

1. Please make the conclusion .

1. Suppose that the standard deviation of the collected data from 121 alumni is \$3k and the mean is \$60k, please estimate the confidence interval of the population’s average salary (10 points, Review PPT Chapter 9). (Hint: Hypothesis Testing and Confidence Interval - One sample; sample standard deviation is known)

95% t = 121-1

t = 1.980

60,000 +/- 1.980(3000/11)

60,000 +/- 540

1. The dean wants to know whether there is salary difference between male and female alumni. He knows that the population standard deviation for male is \$3 and for female is \$4.  The sampled data show that the average salary for 100 male is \$60k and the average salary for 144 female is \$56k (20 points, Review PPT Chapter 11).  (Hint: Hypothesis Testing and Confidence Interval - two samples; population standard deviation is known)
1. What are the null and alternate hypotheses ?

Rule: Reject H0 if z < -1.645 or > 1.645

1. Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) ?

Z = 60,000-56,000 / (9/100 + 16/144)^0.5

Z = 4,000 / .44845

1. What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule .

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