The mean and standard deviation of a random sample of n measurements are equal to 34.1 and 3.7, respectively.

a. Find a 95% confidence interval for if n=64.

b. Find a 95% confidence interval for if n=256.

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficientfixed?

A study on the personality characteristics of drug dealers sampled 100 convicted drug dealers and scored them each on the Wanting Recognition(WR) Scale, which provides a quantitative measure of aperson's need for approval and sensitivity to social situations.(Higher scores indicate a greater need forapproval.) The sample of drug dealers had a mean WR score of 41, with a standard deviation of 7. Use this information to find an interval estimate of the mean WR score for all convicted drug dealers. Use a confidence level of 90%. Interpret the result.

A. The 95% confidence interval for mean WR score indicates that the true mean WR score for all drug dealers is between __ and __ with 95% confidence.

B. The 95% confidence interval for mean WR score indicates that 95% of convicted drug dealers have a WR score between ___ and ___.

C. The 95% confidence interval for mean WR score indicates that the true mean WR score for convicted drug dealers is between ____ and ____ with 95% confidence.

D.

The 95% confidence interval for mean WR score indicates that 95% of all drug dealers have a WR score between ___ and ____.

A random sample of 100 observations from a normally distributed population possesses a mean equal to 85.1 and a standard deviation equal to 5.1. Use this information to complete parts a through e below.

a. Find a 90% confidence interval for .

b. What do you mean when you say that a confidence coefficient is 0.90?

c. Find a 99% confidence interval for

d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is heldfixed?

e.Would your confidence intervals of parts a and c be valid if the distribution of the original population were notnormal? Explain.