Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of1 thousanddollars per employee) for companies in retail sales. Assume3.8thousanddollars.3.5

6.6

3.7

8.9

7.9

5.7

8.5

5.5

1.4

4.3

2.6

5.7

(a) Findxfor the preceding data. (Round your answer to two decimal places.)

thousand dollars per employee=

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit=thousand dollars

upper limit=thousand dollars

(c) Find an 95% confidence interval for, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit=thousand dollars

upper limit=thousand dollars

2.

For this problem, carry at least four digits after the decimal in your calculations.

In a random sample of61professional actors, it was found that35were extroverts.

(a)

Letprepresent the proportion of all actors who are extroverts. Find point estimates forpandq. (Round your answer to four decimal places.)

p=

q=

(b)

Find a96% confidence interval forp.

Find the maximal margin of error. (Round your answer to two decimal places.)

E=

Report the bounds from the96% confidence interval forp. (Round your answers to two decimal places.)

lower limit=

upper limit=

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 4% confident that the true proportion of actors who are extroverts falls above this interval.

We are 96% confident that the true proportion of actors who are extroverts falls outside this interval.

We are 96% confident that the true proportion of actors who are extroverts falls within this interval.

We are 4% confident that the true proportion of actors who are extroverts falls within this interval.

(c)

Do you think the conditionsnp>5 andnq>5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately normal.

Yes, the conditions are satisfied. This is important because it allows us to say thatpis approximately binomial.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately normal.

No, the conditions are not satisfied. This is important because it allows us to say thatpis approximately binomial.