Exam 8: Confidence Interval Estimation

SCENARIO 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 Scenario 8-7, it is possible that the 99% confidence interval calculated from the data will not contain the sample mean number of rooms rented daily in a given month.

SCENARIO 8-6 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product.She samples 120 potential consumers and finds that 54 recognize this product.She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -True or False: Referring to Scenario 8-6, it is possible that the true proportion of people that recognize the product is not between 0.36 and 0.54.

SCENARIO 8-1 The managers of a company are worried about the morale of their employees.In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test.They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. -True or False: Referring to Scenario 8-1, this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

SCENARIO 8-6 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product.She samples 120 potential consumers and finds that 54 recognize this product.She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -True or False: Referring to Scenario 8-6, the parameter of interest to the manager is the proportion of potential customers in this sample that recognize the new product.

The county clerk wants to estimate the proportion of voters who will need special election facilities.The clerk wants to construct a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion.How large a sample must be taken to assure these conditions are met?

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A surveyed 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 Scenario 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.

SCENARIO 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 Scenario 8-8, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

SCENARIO 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 Scenario 8-8, a 99% confidence interval will contain 99% of the student population who own a personal computer.

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 upper end point in a 99% confidence Interval for the average income?

True or False: The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

SCENARIO 8-5 A sample of salary offers (in thousands of dollars)given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59.Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -True or False: Referring to Scenario 8-5, 95% of the time, the sample mean salary offer to management majors will fall between 47.19 and 52.61.

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option.A preliminary sample indicates that the proportion will be around 0.25.Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

True or False: The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

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

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A surveyed 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 Scenario 8-9, we are 99% confident that the total number of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.A surveyed 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 Scenario 8-9, the parameter of interest is the proportion of the student population who feel comfortable reporting cheating by their fellow students.

SCENARIO 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, -True or False: Referring to Scenario 8-4, it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the sample.

SCENARIO 8-11 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. -True or False: Referring to Scenario 8-11, the sampling error is 3%.