Exam 8: Confidence Interval Estimation

If a random sample of size 250 is taken from a population,where it is known that the population proportion p = 0.4,then the mean of the sampling distribution of the sample proportion is 0.60.

The general form of a confidence interval is:

(A)Use Excel to obtain a simple random sample of size 10 from this frame. (B)Using the sample generated in (A),construct a 95% confidence interval for the mean average annual household income level of citizens in the selected U.S.cities.Assume that the population consists of all average annual household income levels in the given frame. (C)Interpret the 95% confidence interval constructed in (B). (D)Does the 95% confidence interval contain the actual population mean? If not,explain why not.What proportion of many similarly constructed confidence intervals should include the true population mean value?

The upper limit of the 90% confidence interval for the population proportion p,given that n = 100; and = 0.20 is 0.2658.

In constructing confidence interval estimate for the difference between the means of two populations,where the unknown population variances are assumed not to be equal,summary statistics computed from two independent samples are as follows: , , , , ,and .Construct 90% confidence interval for .

(A)Construct a 90% confidence interval estimate of the mean family dental expenses for all employees of this corporation. (B)What assumption about the population distribution must be made to answer (A)? (C)Interpret the 90% confidence interval constructed in (A). (D)Suppose you used a 95% confidence interval in (A).What would be your answer? (E)Suppose the fourth value were 593 instead of 93.What would be your answer to (A)? What effect does this change have on the confidence interval? (F)Construct a 90% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation. (G)Interpret the 90% confidence interval constructed in (E).

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size n is greater than 30.

The degrees of freedom for the t and chi-square distributions is a numerical parameter of the distribution that defines the precise shape of the distribution.

(A)You can be 95% confident that the mean salary for all production managers with at least 15 years of experience is between what two numbers (the t-multiple with 8 degrees of freedom is 2.306)? What assumption are you making about the distribution of salaries? (B)What sample size would be needed to ensure that we could estimate the true mean salary of all production managers with more than 15 years of experience and have only 5 chances in 100 of being off by more than $4200?

The mean of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.15,is 15.0.

What would be the t-values where 0.95 of the values would fall within this interval?

In determining the sample size n for estimating the population proportion p,a conservative value of n can be obtained by using 0.50 as an estimate of p.

If two random samples of size 40 each are selected independently from two populations whose variances are 35 and 45,then the standard error of the sampling distribution of the sample mean difference, ,equals 1.4142.

What is the probability of a t-value between -1.40 and +1.40?

(A)Construct a 99% confidence interval for the proportion of company employees who prefer plan A.Assume that the population consists of the preferences of all employees in the frame. (B)Interpret the 99% confidence interval constructed in (A).

A parameter such as is sometimes referred to as a ________ parameter,because many times we need its value even though it is not the parameter of primary interest.

The shape of a chi-square distribution

What is the probability of a t-value larger than 1.20?

Confidence intervals are a function of which of the following three things?

(A)Construct a 90% confidence interval for the total value of all savings account balances within this bank.Assume that the population consists of all savings account balances in the frame. (B)Interpret the 90% confidence interval constructed in (A).