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 ≈ 3.9 thousand dollars.4.36.63.68.87.55.38.45.52.62.98.1−1.911.98.26.44.75.54.83.04.3−6.01.52.94.8−1.79.45.55.84.76.215.04.13.75.14.2(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 μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.) lower limit     thousand dollarsupper 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 μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.) lower limit     thousand dollarsupper limit     thousand dollarsLet 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.

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Asked Jul 7, 2019
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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 ≈ 3.9 thousand dollars.

4.3
6.6
3.6
8.8
7.5
5.3
8.4
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 μ, 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 μ, 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.    
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Expert Answer

Step 1

(a)

Using the provided data, the sample mean can be calculated using Excel function “AVERAGE()”.

  1. Enter the data into Excel sheet.
  2. Use the insert function AVERAGE to find the sample mean as shown below:
fix
E1
AVERAGE(A1:A35)
E
F
A
5.02
1
4.3
6.6
3.6
8.8
5
7.5
5.3
6
Therefore, the sample mean (x is 5.02 thousand dollars per
employee
CO
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Image Transcriptionclose

fix E1 AVERAGE(A1:A35) E F A 5.02 1 4.3 6.6 3.6 8.8 5 7.5 5.3 6 Therefore, the sample mean (x is 5.02 thousand dollars per employee CO

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Step 2

(b)

The 80% confidence interval for the average annual profit per employee for retail sales can be found as follows:

According to provided information
a 3.9, n 35
The z-critical value at 80 % confidence level is,
=-0.s0
- 1.28
Substituting the values in the above formula
3.9
5.02 t 1.28 x -
V35
5.02 +0.84
(4.18,5.86)
Therefore,
Lower limit 4.18 thousand dollars
Upper limit 5.86 thousand dollars
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Image Transcriptionclose

According to provided information a 3.9, n 35 The z-critical value at 80 % confidence level is, =-0.s0 - 1.28 Substituting the values in the above formula 3.9 5.02 t 1.28 x - V35 5.02 +0.84 (4.18,5.86) Therefore, Lower limit 4.18 thousand dollars Upper limit 5.86 thousand dollars

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Step 3

(c)

The annual profit of 3 thousand dollars per employee is less than the lower limit of the 80% confidence interval calculated in part (b). So, the correct option is, ‘Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores’.

 

(d)

The annual profi...

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