Exam 8: Sampling Distributions and Estimation

The Central Limit Theorem (CLT)can be applied to the sample proportion.

The finite population correction factor (FPCF)can be ignored when the sample size is large relative to the population size.

In a survey,858 out of 2600 homeowners said they expected good economic conditions to continue for the next 12 months.Construct a 95 percent confidence interval for "good times" in the next 12 months.

Which statement is most nearly correct,other things being equal?

A sample of size 5 shows a mean of 45.2 and a sample standard deviation of 6.4.The standard error of the sample mean is approximately 2.86.

In constructing a confidence interval,the finite population correction factor (FPCF)can be ignored if samples of 12 items are drawn from a population of 300 items.

To estimate π,you typically need a sample size equal to at least 5 percent of your population.

On the basis of a survey of 545 television viewers,a statistician has constructed a confidence interval and estimated that the proportion of people who watched the season premiere of Glee is between .16 and .24.What level of confidence did the statistician use in constructing this interval? Explain carefully,showing all steps in your reasoning.

The width of a confidence interval for μ is not affected by

In a random sample of 810 women employees,it is found that 81 would prefer working for a female boss.The width of the 95 percent confidence interval for the proportion of women who prefer a female boss is

The standard deviation of the sample proportion p = x/n increases as n increases.

In a large lecture class,the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87.Using the Empirical Rule μ ± 3σ to estimate σ,how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of ±2?

An airport traffic analyst wants to estimate the proportion of daily takeoffs by small business jets (as opposed to commercial passenger jets or other aircraft)with an error of ± 4 percent with 90 percent confidence.What sample size should the analyst use?

In a sample size calculation,if the confidence level decreases,the size of the sample needed will increase.

The sample mean is not a random variable when the population parameters are known.

Jolly Blue Giant Health Insurance (JBGHI)is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy.JBGHI demands a sample large enough to ensure an error of ± 2 percent with 90 percent confidence.What is the necessary sample size?

The standard error of the sample proportion is largest when π = 0.50.

The owner of Limp Pines Resort wanted to know the average age of its clients.A random sample of 25 tourists is taken.It shows a mean age of 46 years with a standard deviation of 5 years.The width of a 98 percent confidence interval for the true mean client age is approximately

Based on the Rule of Three,if no events occur in n independent trials,we can set the upper 95 percent confidence bound at 3/n.

An estimator must be unbiased if you are to use it for statistical analysis.