Exam 8: Large-Sample Estimation

Which of the following best describes an unbiased estimator?

An unbiased estimator of a population parameter is an estimator whose variance is the same as the actual value of the population variance.

What is the type of sample statistic that is used to make inferences about a given type of population parameter?

A 90% confidence interval for the population mean is found to be between 5.28 and 6.72. Based on this information, the sample mean that generated the confidence interval was 6.

Suppose the population standard deviation equals 10. What is the sample size needed to estimate, with 95% confidence, a population mean within 1.5 units of its true value?

A 99% confidence interval estimate for a population mean is determined to be 85.58 to 96.62. If the confidence level is reduced to 90%, what happens to the confidence interval for ?

A statistic is said to be unbiased if its sampling distribution has the smallest standard error.

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. Interpret the confidence interval in the previous question.

The term confidence interval refers to ranges of values among which an unknown population parameter can presumably be found.

Suppose you wish to estimate a population mean based on a random sample of n observations, and prior experience suggests that = 13.2. If you wish to estimate correct to within 1.8, with probability equal to 0.95, how many observations should be included in your sample? Justify your conclusion.

Statisticians routinely construct interval estimates by setting the point estimate as the centre of the interval and then creating a range of other possible values, known as the margin of error, below and above the centre.

The sample standard deviation, s, is an unbiased estimator of the population standard deviation, .

A point estimate of a population parameter will likely be different from the corresponding population value due to the fact that point estimates are subject to sampling error.

In developing an interval estimate for a population mean for which the population standard deviation was 8, the interval estimate was 40.52 3.24. If had equalled 16, what would the interval estimate have been?

Suppose that a 95% confidence interval for the population proportion p is given by . This notation means that we are 95% confident that p falls between and .

When estimating the difference between two population means, one can use the properties of the sampling distribution of two corresponding sample means provided the two samples are selected independently of one another.

If the campaign manager of the Conservative Party is interested in estimating the proportion of voters who will support the Conservative Party in the next federal election, the sample proportion, , would be the appropriate point estimate.

Defective Glass Bottles Narrative A manufacturing plant has two assembly lines for producing glass bottles. The plant manager was concerned about whether the proportion of defective bottles differs between the two lines. Two independent random samples were selected and the following summary data computed: -Refer to Defective Glass Bottles Narrative. Find a 95% confidence interval for the true difference in proportion of defective bottles produced by the two assembly lines.

A simple extension of the estimation of a binomial proportion p is the estimation of the difference between two binomial proportions and .

What is the z-value needed to construct a 92.5% confidence interval estimate for the difference between two population proportions?