Exam 8: Confidence Interval Estimation

Sampling error equals half the width of a confidence interval.

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. -Referring to Scenario 8-11,what is the needed sample size to obtain a 95% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

When determining the sample size necessary for estimating the true population mean,which factor is not considered when sampling with replacement?

SCENARIO 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". -Referring to Scenario 8-9,it is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who feel comfortable reporting cheating by their fellow students.

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. -Referring to Scenario 8-11,you are 99% confidence that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

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. -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.

The confidence interval obtained will always correctly estimate the population parameter.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line.In a sample of 300 items,27 are defective.A 90% confidence interval for the proportion of defectives from this production line would go from _____ to_____ .

The confidence interval estimate of the population proportion is constructed around the sample proportion.

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. -Referring to Scenario 8-11,what is the needed sample size to obtain a 90% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

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 .

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. -Referring to Scenario 8-11,1,500 is the size of the

The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large.

An economist is interested in studying the incomes of consumers in a 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?

In the construction of confidence intervals,if all other quantities are unchanged,an increase in the sample size will lead to an_____ interval.

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

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. -Referring to Scenario 8-11,what is the needed sample size to obtain a 99% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5% if you do not have the information on the 49% in the interviews who said that they would purchase the new game?

SCENARIO 8-10 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Scenario 8-10,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time is .

SCENARIO 8-10 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct.In the survey on 200 managers,58% of the managers have caught salespeople cheating on an expense report,50% have caught salespeople working a second job on company time,22% have caught salespeople listing a "strip bar" as a restaurant on an expense report,and 19% have caught salespeople giving a kickback to a customer. -Referring to Scenario 8-10,we are 95% confident that the population mean number of managers who have caught salespeople cheating on an expense report is between 0.5116 to 0.6484.