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Exam 8: Interval Estimation

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Question 21

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In order to estimate the average electric usage per month, a sample of 196 houses was selected and the electric usage determined. a.Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean. b.With a 0.95 probability, determine the margin of error. c.If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?

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a.25
b.49
...

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Question 22

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In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds. a.Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage. b.Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

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a.17.11 to...

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Question 23

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The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A new brand of breakfast cereal is being market tested. One hundred boxes of the cereal were given to consumers to try. The consumers were asked whether they liked or disliked the cereal. You are given their responses below. a.What is the point estimate of the proportion of people who will like the cereal? b.Construct a 95% confidence interval for the proportion of all consumers who will like the cereal. c.What is the margin of error for the 95% confidence interval that you constructed in part b? d.With a .95 probability, how large of a sample needs to be taken to provide a margin of error of .09 or less?

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is

In developing an interval estimate of the population mean, if the population standard deviation is unknown

A health club annually surveys its members. Last year, 33% of the members said they use the treadmill at least 4 times a week. How large of sample should be taken this year to estimate the percentage of members who use the treadmill at least 4 times a week? The estimate is desired to have a margin of error of 5% with a 95% level of confidence.

Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. -Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately

A local hotel wants to estimate the proportion of its guests that are from out-of-state. Preliminary estimates are that 45% of the hotel guests are from out-of-state. How large a sample should be taken to estimate the proportion of out-of-state guests with a margin of error no larger than 5% and with a 95% level of confidence?

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers revealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval estimate for the average age of all his customers. Assume the population of customer ages is normally distributed.

In determining an interval estimate of a population mean when  is unknown, we use a t distribution with

It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. -Refer to Exhibit 8-3. The 86.9% confidence interval for  is

The mean of the t distribution is

In general, higher confidence levels provide

A university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students discovering that 12 will return for summer school. a.Construct a 90% confidence interval estimate for the proportion of current spring students who will return for summer school. b.With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less?

The degrees of freedom associated with a t distribution are a function of the

Using an   0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

The manager of University Credit Union (UCU) is concerned about checking account transaction discrepancies. Customers are bringing transaction errors to the attention of the bank's staff several months after they occur. The manager would like to know what proportion of his customers balance their checking accounts within 30 days of receiving a transaction statement from the bank. Using random sampling, 400 checking account customers are contacted by telephone and asked if they routinely balance their accounts within 30 days of receiving a statement. 271 of the 400 customers respond Yes. a. Develop a 95% confidence interval estimate for the proportion of the population of checking account customers at UCU that routinely balance their accounts in a timely manner. b. Suppose UCU wants a 95% confidence interval estimate of the population proportion with a margin of error of E = .025. How large a sample size is needed?