Question

1. What effect does raising the level of confidence have on the width of the confidence interval? 2. What effect does lowering the the sample size have on the width of the confidence interval? 3. What effect does a smaller population standard deviation have on the width of the confidence interval? 4. Which of the following is the best interpretation for a 99% confidence interval? 5. Based on prior studies, you believe the standard deviation of IQ is normally distributed with a standard deviation of 16. You obtain a random sample of 85 students in the Columbus metro area and get a sample mean of 102. Construct a 95% CI of the mean IQ of Columbus metro area 6. Acme Manufacturing randomly samples 54 widgets coming off the production line via destructive testing. Four of the widgets were found to be defective. Form a 95% Laplace-Wald CI of the true defect rate 7. Walt suspects his coworker Jesse might be stealing some of his product and wants to compare his actual production yield with what the yield should be. From past experience, he knows the yield of production runs follows a normal distribution. He takes a random sample of the last ten production runs and obtains a sample mean of 2315g and a s.d. of 85g. Form a 98% confidence interval of the true mean production yield

Answer 1

1) Raising confidence level increase critical values which increase margin of error, and hence width increases.

2) Changing the sample size has no effect on the width of the confidence interval.

3) The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 - stronger). The width increases as the significance level decreases (0.5 towards 0.00000...01 - stronger).

4) If we constructed many, many confidence intervals from independent samples of this size, 99% of the time the interval we constructed would capture the true mean.

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