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QNM222 Business Statistics

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  • Course Code: QNM222
  • University: Seneca College
  • Country: Canada

Question:

The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation’s central office during the year. A random sample of 25 clerical workers reveals that12 clerical workers were absent more than 10 days

a)Construct a 95% confidence interval estimate for the proportion of clerical workers absent more than 10 days during the year.

Suppose that the personnel director also wishes to take a survey in a branch office. Answer the following questions:

b)How many clerical workers need to be selected to have 90% confidence in estimating the population proportion to within 0.075 if no previous estimate is available?

c)How many clerical workers need to be selected to have 90% confidence in estimating the population proportion to within 0.075 if the population proportion is estimated to be 0.3?

 

Answer:

Answer 1:

Given that the sample size is 70, population mean is 68.6 and population standard deviation is 8.2. Therefore,

[a] The upper and lower limit of sales is given by 68.58772 and 68.61228.

Particulars

Value

alfa

-0.01253

mean

68.6

Standard deviation

8.2

sample size

70

se

-0.01228

upper limit

68.58772

lower limit

68.61228

[b] Suggested value is not included in the interval though the value is very close to the confidence interval.

[c] With a 95% confidence level, confidence interval will change and will get enlarged. Since the value of confidence level will change so as the added and subtracted amount with the mean. The confidence interval will be as follows:

alfa

-0.06271

mean

68.6

changed se

-15.6297

Changed upper interval

52.97031

Changed lower interval

84.22969

Answer 2:

The sample size is to be calculated within a confidence interval of 95% and standard deviation of 100. The required sample size is 67200.

Particulars

Value

z value

1.68

sd

100

margin of error

0.05

sample size

67200

Answer 3:

 


Given the mean is 290, standard deviation is 125 and sample number is 20. Therefore, The required higher and lower limit is 344.78 and 325.21.

Mean

290

Standard deviation

125

sample size

20

se

54.78367

upper limit

344.7837

lower limit

235.2163

alfa

1.96

Answer 4:

[a] There are in total 25 clerical workers and 12 of them were absent. Therefore, the proportion is absenteeism is 0.48. Then, confidence interval for this proportion is (0.48 ± 0.09) = (0.38,0.57).

Total sample number is

25

Total absent number is

12

Proportion of absenteeism is

0.48

1-p

0.52

z value

1.96

se

0.09992

upper limit

0.57992

lower limit

0.38008

[b] To be estimated population proportion to be 0.75. Therefore, the required sample size is 91.

p

0.75

1-p

0.25

Z value

1.644854

z square

2.705543

n

90.18478

 

91 (appx)

[c] 16 workers needs to be selected to have 90% confidence in estimating the population proportion to be within 0.075.

p

0.3

1-p

0.7

z value

0.640776

nu

0.086225

de

0.005625

nu

15.32883

 

16 (appx)

 
 

References:

Chuosavasdi, T., Stitmannaithum, B., Sumranwanich, T., Saengsoy, W. and Tangtermsirikul, S., 2016. Degree of hydration and mass balance equations for determination of mix proportion of hardened OPC concrete. Engineering Journal (Eng. J.), 20(2), pp.211-219.

Rahayu, W. and Wahyudi, E., 2017. CLASSICAL TEST THEORY OF INNAPROPRIATE INDEX SCORE’S ACCURACY COMPARISON USING CONFUSION MATRIX ACCURACY PROPORTION IN EDUCATIONAL MEASUREMENT. IJER-INDONESIAN JOURNAL OF EDUCATIONAL REVIEW, 4(1), pp.84-92.

TAN, Z. and MA, J., 2017. Evaluation in Imaging of CT System’s Calculation. DEStech Transactions on Computer Science and Engineering, (cii).

Verger, N., Arigliani, M., Raywood, E., Duncan, J.A., Bush, A. and Aurora, P., 2016. P184 Calculation of conductive inhomogeneity in children with severe cf lung disease: which method works?.

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