Exam 8: Large-Sample Estimation

You want to estimate the difference in grade point averages between two groups of college students accurate to within 0.20 grade point, with probability equal to 0.95. If the standard deviation of the grade point measurements is approximately equal to 0.5, how many students must be included in each group? (Assume that the groups will be of equal size.) ______________

A parent believes the average height for 14-year-old girls differs from that of 14-year-old boys. The summary data are listed below where height is in feet. Estimate the difference in the height between girls and boys using a 95% confidence interval. ______________ Based on your interval, do you think there is a significant difference between the true mean height of 14-year-old girls and boys? ______________ Explain. ________________________________________________________

A quality control engineer wants to determine what proportion of defective parts are coming off the assembly line. Past experiments based on large sample sizes show this proportion to be 0.19. What sample size does the engineer need in order to estimate this proportion with a margin of error of 0.12 with 90% confidence? ______________

An unbiased estimator is:

A 95% confidence interval for the population proportion of professional tennis players who earn more than 2 million dollars a year is found to be between .82 and .88. Given this information, the sample size that was used was approximately:

An airline executive estimates that 25% of all flights arrive late. How many flights must we include in a simple random sample if we want to be 90% confident that the true population proportion of flights that arrive late lies within 0.01 of our sample proportion? ______________

The use of the standard normal distribution for constructing confidence interval estimate for the population proportion p requires:

Which of the following statements about the margin of error is false?

A confidence interval for the population proportion p may or may not contain the true value of p.

If the population deviation is known and we wish to estimate the population mean with 95% confidence, what is the appropriate critical value z to use?

A random sample of 45 door-to-door encyclopedia 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 in minutes for the average conversation length. ______________ Give the margin of error. ______________

The maximum distance between an estimator and the true value of a parameter is called the margin of error.

A study conducted by the doctors of a particular hospital involved monitoring a random sample of 75 patients. The results showed it took an average of 3 cc of tranquilizer to put a patient to sleep before surgery with a standard deviation of 0.2 cc. Construct a 95% confidence interval for , the true mean amount of tranquilizer needed to put any patient to sleep. ______________

Some people claim there are health benefits to eating less meat. A health club committee reported the proportion of vegetarians in their city is 0.13. Suppose this estimate was based on a random sample of 80 people. Construct a 99% confidence interval for p, the true proportion of all vegetarian eaters in this particular city. ______________

Suppose you wish to estimate a population mean based on a sample of n observations. What sample size is required if you want your estimate to be within 2 of with probability equal to 0.95 if you know the population standard deviation is 12?

Increasing the confidence level for a confidence interval estimate for the difference between two population means, with all other things held constant, will result in a wider confidence interval estimate.

A statistician knows that the population of light bulb lifetimes is normally distributed and has a standard deviation of 30 hours. A simple random sample of 36 bulbs yields a mean lifetime of 504 hours. Construct a 99% confidence interval for the mean lifetime of all such bulbs. ______________ Interpret the interval. ________________________________________________________

The error of estimation is the distance between an estimate and the estimated parameter.

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

A point estimate is defined as: