Exam 8: Confidence Interval Estimation

True or False: The sampling error can either be positive or negative.

The width of a confidence interval estimate for a proportion will be

TABLE 8-8 The president of a university would like to estimate the proportion of the student population that owns a personal computer.In a sample of 500 students,417 own a personal computer. -True or False: Referring to Table 8-8,a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who own a personal computer is normal.

True or False: Holding the width of a confidence interval fixed,increasing the level of confidence can be achieved with a lower sample size.

True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points,a 90% confidence interval will have a width of 2.36.

The county clerk wants to estimate the proportion of voters who will need special election facilities.Suppose a sample of 400 voters was taken.If 150 need special election facilities,calculate a 90% confidence interval for the population proportion.

TABLE 8-8 The president of a university would like to estimate the proportion of the student population that owns a personal computer.In a sample of 500 students,417 own a personal computer. -True or False: Referring to Table 8-8,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

TABLE 8-13 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Houston.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Table 8-13,what will be the 90% confidence interval for the mean market price of the houses in the suburban county constructed by the consulting group?

TABLE 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students.The results were 1,344 answered "Yes" and 1,456 answered "No." -True or False: Referring to Table 8-9,a 95% confidence interval for the proportion of the student population who feel comfortable reporting cheating by their fellow students is narrower than a 99% confidence interval.

TABLE 8-7 A hotel chain wants to estimate the mean number of rooms rented daily in a given month.The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms. -True or False: Referring to Table 8-7,we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 246.36 and 493.64.

TABLE 8-3 To become an actuary,it is necessary to pass a series of 10 exams,including the most important one,an exam in probability and statistics.An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program.They take a sample of 8 actuarial students in this program and determine that their scores are: 2,5,8,8,7,6,5,and 7.This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. -True or False: Referring to Table 8-3,it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

An economist is interested in studying the incomes of consumers in a particular country.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in a mean income of $15,000.What is the width of the 90% confidence interval?

The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample S = 0.05,the critical value of t will be

An economist is interested in studying the incomes of consumers in a particular country.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in a mean income of $15,000.What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

True or False: The width of a confidence interval equals twice the sampling error.

TABLE 8-7 A hotel chain wants to estimate the mean number of rooms rented daily in a given month.The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms.During February,a sample of 25 days has a sample mean of 370 rooms. -True or False: Referring to Table 8-7,we are 99% confident that between 246.36% and 493.64% of the rooms will be rented daily in a given month.

True or False: Sampling error equals half the width of a confidence interval.

True or False: A sample size of 5 provides a sample mean of 9.6.If the population variance is known to be 5 and the population distribution is assumed to be normal,the lower limit for a 90% confidence interval is 7.96.

True or False: The difference between the sample proportion and the population proportion is called the sampling error.