The World Health Organization is planning a study of the average weight gain of

Question

The World Health Organization is planning a study of the average weight gain of Europeans in the last 5 years. Scientists from the WHO plan on taking a SRS of 100 Europeans and calculating a 95% confidence interval of the average weight gain of all Europeans. The WHO changed their minds and now plans on calculating a 90% confidence interval from the sample they will select. Explain to the WHO the impact of changing their confidence level from 95% to 90%. Select all that apply.

a) The probability of selecting a sample which doesn't capture the true value of would be 10% rather than 5% if they decide to calculate a 90% confidence interval rather than a 95% confidence interval from the sample they will select.

b) They would increase the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.

c) Their confidence interval would be less likely to capture the sample mean.

d) They would decrease the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.

In a recent sample of 31 used cars sales costs, the sample mean was $6,525 with a standard deviation of $3,152. Assume the underlying distribution is approximately normal. Explain what a "95% confidence interval" means for this study.

a) This means that the chances a used car will cost $6,525 is 95%.

b) This means that we are 95% confident that the average cost of used cars in the sample is between the interval values,

c) We are 95% confident that the cost of one new car ranges between the interval values.

d) 95% confidence implies that if intervals are created from repeated samples, 95% of them will contain the true population average cost of a used car.

Explanation / Answer

SOLUTION1:

let say

sample ,mean=5

sd=5

n=64

90% Confidence interval is

5-1.645(5/sqrt(64),5+1.645(5/sqrt(64)

5-1.645(5/8),5+1.645(5/8)

5-1.028,5+1.028

3.972,6.028

95% confidence intyerval is

5-1.96(5/sqrt(64),5+1.96(5/sqrt(64)

3.775,6.225

margin of error=1.96(5/sqrt(64)=1.225

d) They would decrease the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.

For 90% margin of error=1.028

For 95% margin of error=1.225

Decrease of margin of error from 95% to 90%

b) They would increase the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.

OPTIOND

SOLUTION2

Confidence intervals are given for true population parameter

95% confidence implies that if intervals are created from repeated samples, 95% of them will contain the true population average cost of a used car.

ANSWER D

OPTIOND

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