Exam 8: Large-Sample Estimation

Random sample of n = 50 observations from a quantitative population produced = 65.4 and = 2.8. Give the best point estimate for the population mean , and calculate the margin of error.

Twenty retired people living within the Crystal city limits were asked if they would use public transportation if a system was implemented. Their responses are listed below where Y = Yes and N = No. Use these data to estimate p, the true proportion of all retired people living in the city limits who would use a public transportation system, and find the estimated margin of error.

A confidence interval for the population mean will contain the true value of as long as the point estimate is within the lower and the upper confidence limits.

When two independent random samples of sizes and have been selected from populations with means and and variances and , respectively, which of the following is a property of the sampling distribution of ?

Given that n = 400 and = 0.10, the lower limit of the 90% confidence interval for the population proportion p is 0.1247.

It is of interest to know if the average time it takes police to reach the scene of an accident differs from that of an ambulance to reach the same accident. Use the summary data listed below to estimate the difference in the times (measured in minutes) between the police and the ambulance, using a 99% confidence interval. Interpret the meaning of the interval thus obtained. Police: = 60, = 4.2, = 0.08 Ambulance: = 55, = 4.5, = 0.10

A proportion of a basketball team's season ticket holders renew their tickets for the next season. Let p denote the true proportion of ticket holders who buy tickets again for the following season. A random sample of 125 ticket holders revealed 90 people plan on renewing their tickets. Give a point estimate for p and find the estimated margin of error.

For a given sample size and given confidence coefficient, the closer the population proportion p to 1.0, the greater the margin of error will be.

Increasing the sample size, n, will result in a point estimate that is closer to the true value of the population parameter.

A random sample of 45 door-to-door salespersons were asked how long on average they were able to talk to the potential customer. Their answers revealed a mean of 8.5 minutes with a variance of 9 minutes. Give a point estimate for the average conversation length and the margin of error.

Which of the following is NOT a part of the formula for constructing a confidence interval estimate of the population proportion?

A researcher wants to compare the average ages at which men and women first get their driver's licence. A random sample of 75 men yielded a mean and standard deviation of 17.3 and 4.7 years, respectively. A random sample of 96 women yielded a mean and standard deviation of 19.6 and 5.1 years, respectively. If the researcher wants to estimate the mean difference to within 1.5 years with 95% confidence, how large a sample should be taken from each population? (Assume n₁ = n₂ = n.) Justify your conclusion.

If the population variance is increased and other factors remain the same, the width of a confidence interval for the population mean tends to increase.

What would be the lower limit of a confidence interval, at the 95% level of confidence, for the population proportion if a sample of size 100 were to have 30 successes?

If a 90% confidence interval estimate for the difference between two population proportions is to be constructed, what would the confidence coefficient be?

In developing a confidence interval estimate for the difference between two population means, which of the following will result from an increase in the size of the sample?

A sample statistic such that the mean of all its possible values differs from the population parameter that the statistic seeks to estimate is a biased estimator.

An auto mechanic knows that the average time it takes to replace a car radiator is 70 minutes, with a standard deviation of 12 minutes. This average is based on a random sample of 50. Construct a 90% confidence interval for $\mu$ , the true time it takes any auto mechanic to replace a car radiator.

Public versus Private Childcare Expenses Narrative A social worker was interested in determining whether there is a significant difference in the average monthly cost per child for childcare outside the home between publically supported facilities and privately owned facilities. Two independent random samples were selected, yielding the following information: -Refer to Public versus Private Childcare Expenses Narrative. Can one conclude there is a significant difference in the average cost of childcare between the publically supported facilities and the privately owned facilities? Justify your answer.

A sociologist wanted to discover whether there was any difference between Eastern Canadians and Western Canadians in the collective acceptance of multiculturalism as being beneficial to the country. To test the hypothesis that there was essentially no difference, it would be sufficient to collect a convenient sample size from both populations.