Essay on Variance and Random Sample

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Problem Evaluation & Resolution (8730)
Stats Practice Questions
Question 1: The human resource manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers, as many of them do not work for long before quitting. There is a high cost associated with hiring and training new workers and so the manager decided to investigate the factors that influenced his workers to quit. He reviewed the work history of a random sample of workers who have quit in the last year and recorded the number of weeks on the job before quitting and the age of each worker when originally hired. An
Excel analysis was carried out and the Excel output is shown below.
ANOVA
Regression
Residual
Total

Intercept
Age

df
1
78
79

SS
59.51650857
256.4334914
315.95

Coefficients
30.63307456
-0.116916823

Standard Error
1.044141582
0.027478837

MS
F
Significance F
59.51650857 18.10328145 5.76741E-05
3.287608864

t Stat
P-value
29.33804678 6.84876E-44
-4.25479511 5.76741E-05

Lower 95%
28.55434839
-0.171622984

Upper 95%
32.71180074
-0.06221066

(a) Comment on the scatterplot in Figure 1 below, which is for the analysis given above.
Figure 1: Number of Weeks Employed against Age When Originally
Hired

Number of Weeks Employed

32
30
28
26
24
22
20
15

25

35

45

55

Age (years)

(b)
(c)
(d)
(e)
(f)
(g)

a.
What is the dependent variable and what is the independent variable?
Write down the equation of the fitted regression line in standard form.
Use the Excel analysis to test whether there is a negative linear relationship between the age of the workers when originally hired and the number of weeks they stay with the firm. Use  = 0. 01.
Write down a 95% confidence interval for the slope of the fitted regression line. Interpret this interval.
A 40 year old employee worked for 21 weeks. What is the residual for this value?
Comment on the scatterplot in Figure 2 below, which is for the analysis given above. What can you conclude about the validity of the test in part (c)?

1

Figure 2: Residuals against Predicted Values
6

Residuals

4
2
0
-2
-4
-6
24

25

26

27

28

29

Predicted Values

Question 2: An office manager believes that the amount of time spent by office workers reading and deleting spam email exceeds 25 minutes per day. A random sample of 18 workers was selected and the amount of time each spent reading and deleting spam email was measured. The following times (in minutes) were recorded:
35 48 29 44 17 21 32 28 34 23 13 9 11 30 42 37 43 48
Can the office manager conclude that the average time spent reading and deleting spam email is more than 25 minutes? Use  = 0.05.
Question 3: A large production facility uses two machines to produce a key part for its main product.
Sometimes the key part is defective. Inspectors randomly sampled 35 of the key parts from each machine. Of those produced by machine A, 5 were defective. Of those produced by machine B, 7 were defective. Can the production facility conclude that the proportion of defective parts produced by the two machines is different?
Use  = 0.05.
Question 4: At a particular university, administrators believe that the proportion of students preferring to take classes at night exceeds 0.30. To test this, a simple random sample of 200 students is selected and 66 indicate that they prefer night classes.
(a) Can it be concluded that the administrators’ belief is correct? Test using a significance level of 10%. What is the p-value for the test statistic?
(b) What is the p-value for the test in (a)?
Question 5: The supermarket is concerned by complaints by some customers that in the 12 items or less queue some customers have more than 12 items. The supermarket decided to investigate this issue. One morning they watched the first 50 customers and counted the number of items in their baskets.
(a) Assume that the supermarket improved their sampling techniques and from a simple random sample found that 6 out of 50 customers exceeded the item limit in the 12 items or less
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