Quantitative techniques of management-1
QTM Quiz 4
Set A
1. Out of a population of 60 people, the standard error comes to 1.65kg when calculating their average weight using sampling with replacement and 1.61 when using sampling without replacement. What is the sample size and standard deviation of the population? (4)
N=60
With replacement, S.E. =
Without replacement, S.E. = = 1.61
Thus, FPC = (N-n)/(N-1) =
Thus, 60-n = 56.174
Thus, n = 3.8 or 4 approx.
2. When calculating the average income of the residents in a housing complex, how many samples must be taken to ensure the sample mean is within Rs. 10,000 of the original 99% of the time, the standard deviation being Rs.1,00,000? (4)
Thus, and
Thus,
Now, P(|Z|)≥0.99 means P(Z) = 0.995, -2.58 ≤ Z ≤ 2.58,
Thus, 2.58 ≤ 0.1, so n ≥ 665.64 ≈ 666
3. If you are out to measure the most common brand of privately owned automobile in a country, describe how you would set up the experiment, including objective, response variable and sampling type. Justify your answer. (2)
Note: Your answer can be different as long as it is logically presented
Population: All private automobile owners in the country
Objective: To determine the distribution of automobile brands and identify the most common.
Response variable: Brand of automobile privately owned by a person
Sampling process: Use prior judgment and calculations to (a) determine sample size and (b) identify clusters that are representative of the population. Use simple random sampling combined with cluster sampling to gather data on the brands of privately owned automobiles. Following this, perform statistical analysis to determine the most common brand.
QTM Quiz 4
Set B
1. Out of a population of 100 people, the standard error comes to 3.12cm when calculating their average weight using sampling with replacement and 3.07cm when using sampling without replacement. What is the sample size and standard deviation of the population? (4)
N=100
With
Set A
1. Out of a population of 60 people, the standard error comes to 1.65kg when calculating their average weight using sampling with replacement and 1.61 when using sampling without replacement. What is the sample size and standard deviation of the population? (4)
N=60
With replacement, S.E. =
Without replacement, S.E. = = 1.61
Thus, FPC = (N-n)/(N-1) =
Thus, 60-n = 56.174
Thus, n = 3.8 or 4 approx.
2. When calculating the average income of the residents in a housing complex, how many samples must be taken to ensure the sample mean is within Rs. 10,000 of the original 99% of the time, the standard deviation being Rs.1,00,000? (4)
Thus, and
Thus,
Now, P(|Z|)≥0.99 means P(Z) = 0.995, -2.58 ≤ Z ≤ 2.58,
Thus, 2.58 ≤ 0.1, so n ≥ 665.64 ≈ 666
3. If you are out to measure the most common brand of privately owned automobile in a country, describe how you would set up the experiment, including objective, response variable and sampling type. Justify your answer. (2)
Note: Your answer can be different as long as it is logically presented
Population: All private automobile owners in the country
Objective: To determine the distribution of automobile brands and identify the most common.
Response variable: Brand of automobile privately owned by a person
Sampling process: Use prior judgment and calculations to (a) determine sample size and (b) identify clusters that are representative of the population. Use simple random sampling combined with cluster sampling to gather data on the brands of privately owned automobiles. Following this, perform statistical analysis to determine the most common brand.
QTM Quiz 4
Set B
1. Out of a population of 100 people, the standard error comes to 3.12cm when calculating their average weight using sampling with replacement and 3.07cm when using sampling without replacement. What is the sample size and standard deviation of the population? (4)
N=100
With