QNM222 Statistics Homework: Confidence Intervals and Sample Size

This statistics assignment addresses several problems related to confidence intervals and sample size determination. It begins by constructing a 99% confidence interval for the average number of customers at Apache Burger, analyzing whether a manager's suggested value falls within this interval, and discussing how changing the confidence level to 95% would affect the interval. The assignment then calculates the required sample size for a survey on mean family income in a rural area, given a specified confidence level and margin of error. Additionally, it examines absenteeism among clerical workers, determining the proportion of absenteeism and constructing a confidence interval for this proportion. The assignment also calculates the sample size needed to estimate a population proportion with a certain level of confidence and margin of error. The solutions involve applying statistical formulas and concepts to real-world scenarios, providing a comprehensive overview of confidence interval estimation and sample size planning.

Running head: STATISTICS
STATISTICS
Name of the student:
Name of the University:
Author’s note:

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STATISTICS
Table of Contents
Answer 1:.........................................................................................................................................2
[a].................................................................................................................................................2
[b].................................................................................................................................................2
[c].................................................................................................................................................2
Answer 2:.........................................................................................................................................3
Answer 3:.........................................................................................................................................3
Answer 4:.........................................................................................................................................3
[a].................................................................................................................................................3
[b].................................................................................................................................................4
[c].................................................................................................................................................4
References:......................................................................................................................................5

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STATISTICS
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
68.5877
2
lower limit
68.6122
8
[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
1
Changed lower interval
84.2296
9
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

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STATISTICS
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
54.7836
7
upper limit
344.783
7
lower limit
235.216
3
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

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STATISTICS
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)

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STATISTICS
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?.