Exam 8: Interval Estimation

In a random sample of 200 registered voters, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of registered voters in the population who are Democrats.

In general, higher confidence levels provide

A sample of 100 cans of coffee showed an average weight of 13 ounces. The population standard deviation is 0.8 ounces. a.Construct a 95% confidence interval for the mean of the population. b.Construct a 95.44% confidence interval for the mean of the population. c.Discuss why the answers in parts a and b are different.

A random sample of 25 observations was taken from a normally distributed population. The average in the sample was 84.6 with a variance of 400. a.Construct a 90% confidence interval for $\mu$ . b.Construct a 99% confidence interval for $\mu$ . c.Discuss why the 90% and 99% confidence intervals are different. d.What would you expect to happen to the confidence interval in part a if the sample size was increased? Be sure to explain your answer.

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when

A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. She reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. She did not report what confidence coefficient she had used. Based on the above information, determine the confidence coefficient that was used.

If the standard deviation of the lifetimes of vacuum cleaners is estimated to be 300 hours, how large of a sample must be taken in order to be 97% confident that the margin of error will not exceed 40 hours?

National Discount has 260 retail outlets throughout the United States. National evaluates each potential location for a new retail outlet in part on the mean annual income of the households in the marketing area of the new location. National develops an interval estimate of the mean annual income in a potential marketing area after taking a random sample of households.For a marketing area being studied, a sample of 36 households was taken and the sample mean income was $21,100.39. Based on past experience, National Discount assumes a known value of $\sigma$ = $4500 for the population income standard deviation. a. Develop a 95% confidence interval for the mean annual income of households in this marketing area. b. Suppose that National's management team wants a 95% confidence interval estimate of the population mean with a margin of error of E = $500. How large a sample size is needed?

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?

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 $\mu$ is

A random sample of 49 lunch customers was taken at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 33 minutes. From past experience, it is known that the population standard deviation equals 10 minutes. a.Compute the standard error of the mean. b.What can be said about the sampling distribution for the average amount of time customers spent in the restaurant? Be sure to explain your answer. c.With a .95 probability, what statement can be made about the size of the margin of error? d.Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant. e.With a .95 probability, how large of a sample would have to be taken to provide a margin of error of 2.5 minutes or less?

Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for p-bar. In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size recommendation is

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?

In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?

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

Whenever using the t distribution in interval estimation, we must assume that the

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed

In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Candidate A.

To compute the minimum sample size for an interval estimate of $\mu$ , we must first determine all of the following except

When the level of confidence increases, the confidence interval