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 *?* ? 3.6 thousand dollars.

3.7 |
6.9 |
3.6 |
8.0 |
7.5 |
5.4 |
8.8 |
5.5 |
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.)

lower limit | thousand dollars |

upper limit | thousand dollars |

(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.)

lower limit | thousand dollars |

upper limit | thousand dollars |

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.

Answer #1

here sample size=n=35, sample mean=5 and standard deviation=sd=3.6 ( given)

(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)

(b) 80% confidence interval for population mean=sample mean±z(0.2/2)*sd/sqrt(n)

=5±1.28*3.6/sqrt(35)=5±0.78=(4.22, 5.78)

lower limit=4.22 thousand dollar

upper limit=5.78 thousand dollar

(c) Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores.

since the 3 thousand is below the lower limit of confidence interval=4.22 thousand

(d) Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores.

since the 6.5 thousand is above the upper limit of confidence interval=5.78 thousand

(e) 95% confidence interval for population mean=sample mean±z(0.5/2)*sd/sqrt(n)

=5±1.96*3.6/sqrt(35)=5±1.19=(3.81, 6.19)

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 1
thousand dollars per employee) for companies in retail sales.
Assume σ ≈ 4.0 thousand dollars.
3.8
6.5
4.3
8.9
7.5
5.7
8.5
5.7
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...

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 1
thousand dollars per employee) for companies in retail sales.
Assume σ ≈ 4.2 thousand dollars. 3.5 6.7 3.6 8.1 7.6 5.7 8.8 6.0
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...

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 1
thousand dollars per employee) for companies in retail sales.
Assume ? ? 3.7 thousand dollars.
4.5
6.2
4.3
8.7
8.1
5.7
9.0
6.4
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...

Jobs and productivity! How do banks rate? One way to answer this
question is to examine annual profits per employee. The following
is data about annual profits per employee (in units of 1 thousand
dollars per employee) for representative companies in financial
services. Assume σ ≈ 10.2 thousand dollars.
25.7
39.0
34.8
25.7
58.6
45.3
34.1
39.7
42.5
33.0
33.6
36.9
27.0
47.1
33.8
28.1
28.5
29.1
36.5
36.1
26.9
27.8
28.8
29.3
31.5
31.7
31.1
38.0
32.0
31.7
32.9...

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 1
thousand dollars per employee) for companies in retail sales.
Assume σ ≈ 3.8 thousand dollars.
4.0 6.2 3.8 9.0 8.0 5.1 8.4 6.5 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...

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 σ ≈ 3.7 thousand dollars.
3.5
6.6
3.6
9.0
7.7
5.1
8.6
6.3
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...

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 σ ≈ 3.6 thousand dollars.
4.4
6.0
4.5
8.4
8.5
5.0
9.0
6.5
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...

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 σ ≈ 3.8 thousand dollars.
4.0
6.9
4.5
9.0
7.5
5.8
8.2
5.6
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...

Jobs and productivity! How do banks rate? One way to answer this
question is to examine annual profits per employee. The following
is data about annual profits per employee (in units of 1
thousanddollars per employee) for representative companies in
financial services. Assume ? ? 9.9 thousanddollars.
54.4
45.3
48.8
60.0
31.3
39.0
29.9
44.6
42.5
33.0
33.6
36.9
27.0
47.1
33.8
28.1
28.5
29.1
36.5
36.1
26.9
27.8
28.8
29.3
31.5
31.7
31.1
38.0
32.0
31.7
32.9
23.1
54.9...

A.) What price do farmers get for their watermelon crops? In the
third week of July, a random sample of 42 farming regions gave a
sample mean of x = $6.88 per 100 pounds of watermelon.
Assume that ? is known to be $1.98 per 100 pounds.
Find the sample size necessary for a 90% confidence level with
maximal error of estimate E = 0.45 for the mean price per
100 pounds of watermelon. (Round up to the nearest whole...

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