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• Course Code: QNM222
• University: Seneca College

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?

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 52.9703 Changed lower interval 84.2297

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

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 54.7837 upper limit 344.784 lower limit 235.216 alfa 1.96

[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?.

Cite This Work

[Accessed 11 August 2020].

My Assignment Help. 'Business Statistics' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/qnm222-business-statistics> accessed 11 August 2020.

My Assignment Help. Business Statistics [Internet]. My Assignment Help. 2020 [cited 11 August 2020]. Available from: https://myassignmenthelp.com/free-samples/qnm222-business-statistics.

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