1.It has been reported that the average credit card debt for college seniors at

Question

1.It has been reported that the average credit card debt for college seniors at the college book store for a specific college is $3262. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and finds that the average debt is $2995, and the population standard deviation is $1100. With a significance of 0.05, is the student senate correct?

a.What is the critical value (z or t score) for this problem?

b.What is the test statistic value in step 3?

c.What is our decision for step 4?

d.What is your decision?

2.Nationwide, the average salaries of actuaries who achieve the rank of Fellow is $150,000. An insurance executive wants to see how this compares with Fellows within his company. He checks the salaries of eight Fellows and finds the average salary to be $155,500 with a standard deviation of $15,000. Can he conclude that Fellows in his company make more than the national average, using a significance of 0.05?

a.What is the alternative hypothesis in step 1?

b.What is the critical value from step 2?

c.What is the test statistic value for step 3?

d.Do we reject or fail to reject H0 and what does that indicate (step 4 and 5)?

Explanation / Answer

1)

Hypothesis:

H0 : mu > = 3262

Ha: mu < 3262

2) Critical value for 0.05 = -1.64

3) Test statistic:

z = ( 2995 - 3262) / ( 1100 / sqrt(50))

= -1.72

Now, we need to find p value using z= -1.72

p value = 0.042716.

4) As, p value is less than alpha =0.05

So. we reject the null hypothesis.

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