what is the answer for 3c 4d 5a 7d 3 A simple random sample

3) A simple random sample of 60 jtems resulted in a sample mean of 80, The standard deviation is 15. a Compute the 95% confidence interval for the population mean. b. Assume that the same sample mean was obtained from a sample of 120 items. a 95% confidence interva!for the population mean. Whatis the effect of a larger avalestinan R c. te iet aflager smple size on then sample size on the interval estimate? simple random sample with n 54 provided a sample mean of 22.5 and a sample stan- deviation ot 44 Develop a 90% confidence interval for the population mean. Develop a 95% confidence interval for the population mean. Develop a 99% confidence interval for the population mean. What happens to the margin of error and the confidence interval as the confidence level is increased? b. c. d. The National Quality Research Center at the University of Michigan provides a qui terly measure of consumer opinions about products and services (The Wall Street Jourd February 18, 2003). A survey of 10 restaurants in the Fast Food/Pizza group showed sample mean customèr satisfaction index of 71. Past data indicate that the population dard deviation of the index has been relatively stable with 5. a. What assumption should the researcher be willing to make if a margin of error is desin b. Using 95% confidence, what is the margin of error? 5 what is the margin of error if 99% confidence is desired? @jEnd i. Sales personnel for Skillings Distributors submit weekly reports listing the customer con- ts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel. Playbill magazine reported that the mean annual household income of its readers $119,155 (Playbill, January 2006). Assume this estimate of the mean annual household come is based on a sample of 80 households and, based on past studies, the population stai dard deviation is known to be -$30,000. Develop a 90% confidence interval estimate of the population mean. Develop a 95% confidence interval estimate of the population mean. Develop a 99% confidence interval estimate of the population mean. d. Discuss what happens to the width of the confidence interval as the confidence levee is increased. Does this result seem reasonable? Explain.

Solution

3c)

A LARGER SAMPLE SIZE will make the interval NARROWER.

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4d)

The margin of error will increase, and the confidence interval will then be wider.

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5a.

He should assume the the population is normally distrbuted, and that the sample he has is a simple random sample.

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7d.

As confidence level increase, the interval widens. This is reasonable because if you want to be more confidence that you have the true mean in your interval, you should widen your interval.