Exam 8: Large-Sample Estimation

Increasing the confidence coefficient from 0.90 to 0.95 and decreasing the sample size from 100 to 50 has unknown impact on the margin of error.

If the population deviation is known and we wish to estimate the population mean with 95% confidence, which of the following would be the appropriate critical z-value to use?

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. Find a 90% confidence interval for the true difference in average monthly cost of childcare between publically supported and privately owned facilities.

Instead of paying to support welfare recipients, many people want them to find jobs. If necessary, they want each province to create public service jobs for those who cannot find jobs in private industry. In a survey of 800 voters, 400 Conservatives and 400 Liberals, 75% of the Conservatives and 90% of the Liberals favoured the creation of public service jobs. Use a large-sample estimation procedure to compare the difference between the proportions of Conservatives and Liberals who favour creating public service jobs in the population of registered voters. Explain your conclusions.

Childcare Expenses Narrative A childcare agency was interested in examining the average amount that families pay per child per month for childcare outside the home. A random sample of 64 families was selected and the mean and standard deviation were computed to be $675 and $80, respectively. -Refer to Childcare Expenses Narrative. Interpret the interval in the previous question.

Which of the following best describes an interval estimate?

The manufacturer of a particular battery pack for a laptop computer claims the battery pack can function for eight hours, on average, before having to be recharged. A random sample of 36 such battery packs was selected and tested. The mean and standard deviation were found to be 6 hours and 1.8 hours, respectively. Find a 95% lower confidence bound for the true average time the battery pack can function before having to be recharged. Interpret this bound.

Telephone Poll Radio and television stations often air controversial issues during broadcast time and ask viewers to indicate their agreement or disagreement with a given stand on the issue. A poll is conducted by asking those viewers who agree to call a certain 900 telephone number and those who disagree to call a second 900 telephone number. All respondents pay a fee for their calls. -Please refer to Telephone Poll paragraph. What can be said about the validity of the results of such a survey? Do you need to be concerned about a margin of error in this case? Justify your conclusion.

A 90% confidence interval estimate for a population mean is determined to be 62.8 to 73.4. If the confidence level is reduced to 80%, the confidence interval for becomes narrower.

In a study of the relationship between birth order and university success, an investigator found that 140 in a sample of 200 university graduates were firstborn or only children. In a sample of 120 nongraduates of comparable age and socioeconomic background, the number of firstborn or only children was 66. Estimate the difference between the proportions of firstborn or only children in the two populations from which these samples were drawn. Use a 90% confidence interval and interpret your results.

Childcare Expenses Narrative A childcare agency was interested in examining the average amount that families pay per child per month for childcare outside the home. A random sample of 64 families was selected and the mean and standard deviation were computed to be $675 and $80, respectively. -Refer to Childcare Expenses Narrative. Find a 95% confidence interval for the true average amount spent per child per month for childcare outside the home.

A 95% confidence interval for the population proportion p is found to be between 0.214 and 0.336. Based on this information, the sample proportion that generated the confidence interval was 0.122.

What is a sample statistic such that the mean of all its possible values differs from the population parameter that the statistic seeks to estimate?

If a population is right skewed, the point estimate will be pushed to the right of the middle of the confidence interval estimate.

A random sample of 60 people revealed that it took an average of 55 minutes, with a standard deviation of 10 minutes, for a person to complete a loan application at the bank. Construct a 90% confidence interval for $\mu$ , the true time it takes any person to complete the loan form.

An interval estimate is an estimate of the range for a sample statistic.

A researcher wants to determine the proportion of elm trees in Windsor, Ontario, dying of Dutch elm disease. Past experiments, based on large sample sizes, have shown this proportion to be 0.3. What sample size does the researcher need in order to estimate this proportion to within 0.04 with 95% confidence? Justify your conclusion.

Ground Beef Weights Narrative The meat department of a local supermarket packages ground beef using meat trays of two sizes: one designed to hold approximately 700 g of meat, and a larger one that holds approximately 1.4 kg. A random sample of 36 packages of the smaller meat trays produced weight measurements with an average of 715 g and a standard deviation of 90 g. -Refer to Ground Beef Weights Narrative. What does the phrase "99% confident" mean?

Which of these options provides the best interpretation of a 90% confidence interval estimate of the population mean ?

Trish attends a yoga class four times each week. She would like to estimate the mean number of minutes of continuous exercise until her heart reaches 90 beats per minute. If it can be assumed that $\sigma$ = 1.7 minutes, how large a sample is needed so that it will be possible to assert with 99% confidence that the sample mean has a margin of error of, at most, 0.62 minutes? Justify your conclusion.