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a) Battery life for a hand-held computer is normally distrbuted and has a population standard deviation of 3 hours. Suppose you need to estimate a confidence interval estimate at the 95% level of confidence for the mean life of these batteries. Determine the sample size required to have a margin of error of 0.253 hours. Round up to the nearest whole number.
b)The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction which has a known standard deviation of 24 points. They should sample employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.
c) Suppose a department store wants to estimate the average age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 0.95. Management believes that the standard deviation is 8 years. The sample size they should take is .

Sagot :

KhiradAfaq

(a) The required sample size is 1.96.

(b) Sample size = n = 89

(c) Sample size = n = 62

What is standard deviation?

The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

(a) Population standard deviation = σ = 3

Margin of error = E = 0.253

At 95% confidence level the z is,

α = 1 - 95%

α = 1 - 0.95 = 0.05

α/2 = 0.025

Zα/2 = 1.96

sample size = n = [Zα/2* σ / E]^2

n = [1.96 * 3 / 0.253]2

n = 540.14

Sample size = n = 541

b) Population standard deviation = σ = 24

Margin of error = E = 5

sample size = n = [Zα/2* σ/ E] 2

n = [1.96 * 24 / 5]2

n = 88.51

Sample size = n = 89

c) Population standard deviation = σ = 8

Margin of error = E = 2

sample size = n = [Zα/2* σ / E] 2

n = [1.96 * 8 / 2]2

n = 61.46

Sample size = n = 62

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