Exam #3

In a survey of 1037 US adults ages 65 and over, 643 were concerned about getting the flu. A 99% confidence interval for the proportion p of US adults ages 65 and over concerned about getting the flu is closest to

(.5813, .6589)

In a survey of 2563 adults from France, 1666 said that they believed that the activities of humans are contributing to an increase in global temperatures. A 95% confidence interval for the proportion p of adults in France, who think humans are contributing to an increase in global temperatures, is closest to:

(.6315, .6685)

Suppose that you have a sample size n = 100 with mean x = 5 and standard deviation s = 2, and that you are to construct a confidence interval for the population mean \mu μ . A 95% confidence interval for \mu\: μ is closest to:

(4.608, 5.392)

To estimate the mean retail price of designer jeans, a buyer sampled 19 retailers in New York City and recorded the selling price of the jeans. The following statistics were reported: x = 51.75 dollars, and s = 5.50 dollars. Assuming the prices at different retailers are normally distributed, a 99% confidence interval for the mean is closest to:

(48.12, 55.38)

A random sample of 100 observations produced a mean x = 50 and a standard deviation s = 5. Find a 97% confidence interval for the population mean \mu μ (round off to two decimal).

(48.92, 51.09)

A car dealer wants to get information about the number of years car owners keep their cars. A random sample of 25 car owners resulted in x = 7.01 years, and s = 3.74 years. Assume that the sample is drawn from a normally distributed population. Construct a 95% confidence interval for the mean number of years of car ownership.

(5.47, 8.55)

In a random sample of 15 computers, the mean repair cost was $100 and the standard deviation was $42.50. Assume that the repair cost of computers follows a normal distribution. Construct a 95% confidence interval for \mu μ , the mean repair cost of computers.

(76.46, 123.54)

In order to estimate the proportion of office workers who listen to streamed music on a work computer on a regular basis, a sample of 1200 office workers who work at a computer was taken. Of them, 543 listen to streamed music on the computer at work. A 99% confidence interval for the proportion of all office workers who listen to streamed music at work is about:

.453 ± .037

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg. Let p denote the proportion of all cartons which have at least one broken egg. Find a point estimate for p and also construct a 90% confidence interval for p.

0.12, (0.086, 0.154)

The manager of the dairy section of a large supermarket chose a random sample of 300 egg cartons and found that 48 cartons had at least one broken egg. Let p denote the proportion of all cartons which have at least one broken egg. Find a point estimate for p and also construct a 90% confidence interval for p.

0.160, (0.125, 0.195)

In a random sample of 1,300 recent college graduates, 238 had students loan totaling at least $25,000 when they graduated. A 99% confidence interval for the proportion of all graduates with at least $25,000 in student loans when they graduated is about

0.18 \pm ± 0.03

In a clinical trial, 200 patients who received a new medication are randomly selected. It was found that 40 of them suffered serious side effects from this new medication. Let p denote the population proportion of patients suffered serious side effects from this new medication. Find a point estimate for p and also construct a 95% confidence interval for p.

0.20, (0.145, 0.255)

In a survey of 1000 people, 700 people said that they voted in the last presidential election. Let p denote the proportion of all people who voted. Find a point estimate for p and also construct a 90% confidence interval for p.

0.700, (0.676, 0.724)

Measurement of the waiting time of 45 randomly selected patients at a hospital emergency room gave mean and standard deviation 11.3 and 6.5 minutes. A 90% confidence interval for the mean waiting time of all patients is about

11.3+(1.645)(6.5/SQUAREROOT45)

A machine is supposed to cut plastic into sheets that are 600 inches long, The company wants to estimate the mean length the machine is cutting the plastic, accurate to within 0.04 inch. Determine the sample size required to construct a 92% confidence interval. Assume that the population is normal with a standard deviation of 0.25 inch.

120

A college administrator would like to estimate the average grade point average (average of GPA) of all the current registered students based on a random sample. He plans to estimate the average GPA to within 0.05 with 90% confidence interval. At least how many students does he need to include in the sample in order to accomplish that? Assume the standard deviation of all GPA's in the student population is \sigma σ = 0.4.

174

A researcher wishes to estimate the average number of hours of sleep working adults get each night, at 90% confidence and to within 10 minutes (1/6 hour). On the assumption that the population standard deviation is 1.5 hours, the minimum size of the sample needed is about:

220

Fifty randomly selected individuals were timed completing a tax form. The sample mean was 23.6 minutes; the sample standard deviation was 2.4 minutes. A 99% confidence interval for the mean time required by all individuals to complete the form is about:

23.6+.87

An economist wishes to estimate the proportion of household income spent on energy (gas, electricity, and so on), at 95% confidence and to within five percentage points. Assuming no prior knowledge of the true proportion the minimum sample size needed is about

385

How large a sample is required to obtain a 99% confidence interval for the proportion of all newborns who are breast-fed exclusively in the first two months of life to within 2 percentage points?

4148

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg. Let p denote the proportion of all cartons which have at least one broken egg. Based on the preliminary estimate for p from the above sample, find the minimum sample size needed to estimate to population proportion p with 85% confidence. The estimate must be accurate to within .02 of p.

548

In a clinical trial, 200 patients who received a new medication are randomly selected. It was found that 40 of them suffered serious side effects from this new medication. Let p denote the population proportion of patients suffered serious side effects from this new medication. Using the information from the above sample, find the minimum sample size needed to estimate the population proportion p with 80% confidence. The estimate must be accurate to within .02 of p.

656

A company wants to estimate the mean time (in hours) per week for an adult who uses computers at home. Find the minimum sample size needed in order to construct a 97% confidence interval for the mean time of computer usage at home for an adult, to within 0.25 hours. The company assumes \sigma σ is 1 hour.

76

Given that the population standard deviation is \sigma σ = 1, determine the minimum sample size needed in order to estimate the population mean so that the margin of error is E = .2 at 95% level of confidence.

97

In a survey of 1000 people, 700 people said that they voted in the last presidential election. Let p denote the proportion of all people who voted. Which of the following actions would result in a confidence interval narrower than the 90% confidence interval computed above?

Computing a 80% confidence interval rather than a 90% confidence interval

The manager of the dairy section of a large supermarket chose a random sample of 300 egg cartons and found that 48 cartons had at least one broken egg. Let p denote the proportion of all cartons which have at least one broken egg. Which of the following actions would result in a confidence interval wider than the 90% confidence interval computed above?

Computing an 95% confidence interval rather than a 90% confidence interval

Suppose that you have a sample size n = 100 with mean x = 5 and standard deviation s = 2, and that you are to construct a confidence interval for the population mean \mu μ . If, after you obtain the confidence interval, you find it to be too wide, which of the following remedial steps can you take to reduce the width of the confidence interval? I. To construct a 90% confidence interval instead of a 95% one. II. To construct a 99% confidence interval instead of a 95% one. III. To re-do the 95% confidence interval with only a half pf the sample data.

I only

A car dealer wants to get information about the number of years car owners keep their cars. A random sample of 25 car owners resulted in x = 7.01 years, and s = 3.74 years. Assume that the sample is drawn from a normally distributed population. All other information remaining unchanged, which of the following would produce a wider interval than the 95% confidence interval constructed?

The sample size is 10 instead of 25

In a random sample of 15 computers, the mean repair cost was $100 and the standard deviation was $42.50. Assume that the repair cost of computers follows a normal distribution. All other information remaining unchanged, which of the following would produce a narrower interval than the 95% confidence interval constructed?

The sample size is 28 instead of 15

An economist wants to estimate the mean income during the first years of employment for a college graduate who has had a statistic course. Find the minimum sample size needed to estimate the mean \mu μ with 88% confidence. The estimate must be accurate to within $500 of \mu μ . Assume \sigma σ = $6250

n = 378