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Quiz 4 Solved New

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Quiz 4 Solved New
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  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 srcinal 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 replacement, S.E. = √    Without replacement, S.E. = √  √   = 3.07 Thus, FPC = (N-n)/(N-1) = (  )   Thus, 100-n = 95.852 Thus, n = 4.15 or 4 approx. √   2.   When calculating the average house rent of the residents in a district, how many samples must be taken to ensure the sample mean is within Rs. 2,000 of the actual mean 95% of the time, the standard deviation being Rs.5,000? (4) ̅  Thus,  ̅√   √    and    Thus, √    Now, P(|Z|)≥0.95 means P(Z) = 0.975, - 1.96 ≤ Z ≤ 1.96,   Thus, 1.96 ≤ 0.4 √  , so n   ≥ 24.01 ≈  25   3.   If you are out to measure the most market share of a toothpaste brand among under-21s in a city, 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 under-21s in the city Objective: To determine the proportion of the population (under-21s in the city) that uses a certain toothpaste brand. Response variable: Brand of toothpaste used by a person under 21 years of age Sampling process: Use prior judgment to identify geographical locations with a high percentage of under-21s (schools, colleges, sports clubs etc.), thus reducing the cost of reaching a large sample of the target population. Use stratified random sampling (each location being a strata) to determine the toothpaste brand used by respondents, followed by statistical analysis to identify the proportion, and thus market share, of the brand we are interested in.
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