Jobs and productivity! How do retail stores rate? One way to answer this questio
ID: 2906670 • Letter: J
Question
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 of one thousand dollars per employee) for companies in retail sales. Assume ? ? 3.5 thousand dollars.
4.2
6.3
3.5
8.0
7.8
5.6
8.0
5.8
2.6
2.9
8.1
?1.9
11.9
8.2
6.4
4.7
5.5
4.8
3.0
4.3
?6.0
1.5
2.9
4.8
?1.7
9.4
5.5
5.8
4.7
6.2
15.0
4.1
3.7
5.1
4.2
(a) Use a calculator or appropriate computer software to find x for 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.)
(c) Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part (b).
Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.
(d) Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b).
Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.
(e) Find an 95% confidence interval for ?, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)
Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part (b).
Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.
Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b).Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores.No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.
2.
8.2/7 points | Previous AnswersBBUnderStat11 7.1.018.
Ask Your Teacher
Ask your teacher mmessage sent
My Notes
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 45 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that ? is known to be $1.86 per 100 pounds.(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)
4.2
6.3
3.5
8.0
7.8
5.6
8.0
5.8
2.6
2.9
8.1
?1.9
11.9
8.2
6.4
4.7
5.5
4.8
3.0
4.3
?6.0
1.5
2.9
4.8
?1.7
9.4
5.5
5.8
4.7
6.2
15.0
4.1
3.7
5.1
4.2
Explanation / Answer
SolutionA:
(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars per employee
annualprofits <- c(4.2,6.3,3.5,8,7.8,5.6,8,5.8,2.6,2.9,8.1,-1.9,11.9,
8.2,6.4,4.7,5.5,4.8,3,4.3,-6,1.5,2.9,4.8,-1.7,9.4,5.5,
5.8,4.7,6.2,15,4.1,3.7,5.1,4.2)
mean(annualprofits)
mean=5
Solutionb:
sigma=3.5
alpha=1-0.80=0.2
alpha/2=0.2/2=0.1
Z crit=1.281552
80% confidence interval for mean
=xbar-Zsigma/sqrt(n),xbar+z sigma/sqrt(n)
=5-1.281552*3.5/sqrt(35),5+1.281552*3.5/sqrt(35)
=4.24,5.76
lower limit=4.24
upper limit=5.76
e) Find an 95% confidence interval for ?, the average annual profit per employee for retail sales.
z crit for 95%=1.96
95% confidence interval for mean
=xbar-Zsigma/sqrt(n),xbar+z sigma/sqrt(n)
=5-1.96*3.5/sqrt(35),5+1.96*3.5/sqrt(35)
=3.84,6.16
LOWER LIMIT=3.84
UPPER LIMIT=6.16
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.