A preliminary sample of holiday shoppers revealed that the standard deviation of

Question

A preliminary sample of holiday shoppers revealed that the standard deviation of the amount of money they are planning to spend on gifts during the coming holiday season is $76. How many holiday shoppers should be sampled in order to estimate the average amount of money spent on gifts by all holiday shoppers with a margin of error of $5 and with a 90% confidence? a. 371 b. 921 c. 626 d. 584 A machine produces a part for the automotive industry. 6% of the parts produced were defective in the past, and we believe that the current percentage is not higher. What is the needed sample size for estimating the current percentage of defective parts with the 95% confidence and the 2% margin of error? a. 310 b. 611 c. 216 d. 542 We are interested in conducting a study to determine what percentage of eligible voters will support the incumbent governor in the coming election. Recent polls have indicated that the support changes drastically every week. What is the minimum sample size needed to estimate this percentage with a margin of error of 5% and a 95% confidence?

Explanation / Answer

Answer:

15).

Sample size calculation

p=0.5( we assume)

For 95%, z=1.96

d=0.05

Sample size = (z2*p*(1-p))/d2

= (1.962*0.5*0.5)/0.052

=384.16

The sample size required= 385

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