Exam 8: Confidence Interval Estimation

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. -Referring to Table 8-8,a 95% confidence interval for the proportion of the student population who own a personal computer is narrower than a 99% confidence interval.

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. -Referring to Table 8-8,it is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who own a personal computer.

Suppose a 95% confidence interval for μ has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval,then the resulting interval width would ________.(Assume that the sample statistics gathered would not change very much for the new sample.)

A sample of 100 fuses from a very large shipment is found to have 10 that are defective.The 95% confidence interval would indicate that,for this shipment,the proportion of defective fuses is between 0 and 0.28.

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. -Referring to Table 8-3,a 90% confidence interval for the mean score of actuarial students in the special program is from ________ to ________.

TABLE 8-9 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Table 8-9,the superintendent can conclude with 95% level of confidence that no more than 5% of the students in the unified school district skipped more than 10 days of school last year.

The sample mean is a point estimate of the population mean.

TABLE 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Table 8-4,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

TABLE 8-9 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Table 8-9,what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

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 24 rooms.During February,a sample of 25 days has a sample mean of 37 rooms. -Referring to Table 8-7,the parameter of interest is the mean number of rooms rented daily in a given month.

TABLE 8-14 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months.Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game.The margin of error was ±3 percentage points. -Referring to Table 8-14,the standard error is 3%.

A 99% confidence interval estimate can be interpreted to mean that

TABLE 8-14 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months.Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game.The margin of error was ±3 percentage points. -Referring to Table 8-14,you are 99% confidence that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

TABLE 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Table 8-4,a confidence interval for this sample would be based on the t distribution with ________ degrees of freedom.

TABLE 8-10 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Table 8-10,using the 90% one-sided confidence interval,the president can be 95% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

TABLE 8-10 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Table 8-10,what is the critical value for the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

A prison official wants to estimate the proportion of cases of recidivism.Examining the records of 250 convicts,the official determines that there are 65 cases of recidivism.A confidence interval will be obtained for the proportion of cases of recidivism.Part of this calculation includes the estimated standard error of the sample proportion.For this sample,the estimated standard error is ________.

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known,regardless of the shape of the distribution in the population.

For a t distribution with 12 degrees of freedom,the area between -2.6810 and 2.1788 is 0.980.

The difference between the sample mean and the population mean is called the sampling error.