Exam 8: Confidence Interval Estimation

Instruction 8-5 The actual voltages of power packs labelled as 12 volts are as follows: 11.77,11.90,11.64,11.84,12.13,11.99,and 11.77. -Referring to Instruction 8-5,a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

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 99% confidence interval for the proportion of cases of recidivism would go from ________ to ________.

Instruction 8-13 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". -Referring to Instruction 8-13,a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is from ________ to ________.

Instruction 8-10 The Registrar of a university would like to estimate the proportion of the student population who owns a personal computer.In a sample of 500 students,417 own a personal computer. -Referring to Instruction 8-10,we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

Instruction 8-12 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 Instruction 8-12,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?

Instruction 8-1 A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results. -Referring to Instruction 8-1,there are 10 possible samples of 100 stores that can be selected out of the population of 1,000 stores.

Instruction 8-10 The Registrar of a university would like to estimate the proportion of the student population who owns a personal computer.In a sample of 500 students,417 own a personal computer. -Referring to Instruction 8-10,the parameter of interest is the average number of students in the population who own a personal computer.

Instruction 8-12 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 Instruction 8-12,the standard error is 3%.

Instruction 8-4 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 Instruction 8-4,it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special class.

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

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

Instruction 8-3 A quality control engineer is interested in the mean length of timber poles being cut automatically by machine.The desired length of the insulation is 12 metres.It is known that the standard deviation in the cutting length is 0.15 metres.A sample of 70 cut poles yields a mean length of 12.14 metres.This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. -Referring to Instruction 8-3,the confidence interval is valid only if the lengths cut are normally distributed.

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

A race car driver tested his car for time from 0 to 100 km/h,and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 100 time is 4.52 seconds to 5.18 seconds.

Instruction 8-14 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 Instruction 8-14,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is ________.