Exam 8: Confidence Interval Estimation

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,of all possible samples of 100 stores drawn from the population of 1,000 stores,95% of the sample means will fall between 5.623 and 6.377 lawnmowers.

Instruction 8-19 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 8-19,a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who feel comfortable reporting cheating by their fellow students is normal.

Instruction 8-19 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 8-19,the parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

Instruction 8-10 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 8-10,a confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

In forming a 90% confidence interval for a population mean from a sample size of 22,the number of degrees of freedom from the t distribution equals 22.

It is desired to estimate the average total compensation of CEOs in the Service industry.Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260,$5,836,180) -Which of the following interpretations is correct?

The sampling error can either be positive or negative.

It is desired to estimate the average total compensation of CEOs in the Service industry.Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260,$5,836,180). -Based on the interval above,do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?

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 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

Instruction 8-20 A business and management magazine conducted a survey on employees cheating on their expense reports and other unethical conduct. In the survey of 200 managers, 58% of the managers have caught employees cheating on an expense report, 50% have caught employees working a second job on company time, 22% have caught employees listing a "strip bar" as a restaurant on an expense report, and 19% have caught employees giving a kickback to a customer. -Referring to Instruction 8-20,the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught employees giving a kickback to a customer is ________.

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 ________.

The t distribution

As an aid to the establishment of personnel requirements,the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period.The director randomly selects 64 different 24-hour periods and determines the number of admissions for each.For this sample, $\bar { X }$ = 19.8 and S² = 25.Using the sample standard deviation as an estimate for the population standard deviation,what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?

Instruction 8-14 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognise a new product. She samples 120 potential consumers and finds that 54 recognise this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -Referring to Instruction 8-14,it is possible that the true proportion of people that recognise the product is not between 0.36 and 0.54.

A private university is considering a change in the way students pay for their education.Presently the students pay $55 per credit hour.The university system administrators are contemplating charging each student a set fee of $750 per quarter,regardless of how many credit hours each takes.To see if this proposal would be economically feasible,the administrators would like to know how many credit hours,on the average,each student takes per quarter.A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter.Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation.How large a sample would they need to take?

Instruction 8-8 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 8-8,you are 99% confident that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

An officer with the Australian Electoral Office wants to estimate the proportion of retired voters who will need special election facilities.Suppose a sample of 400 retired voters was taken.If 150 need special election facilities,calculate a 90% confidence interval for the population proportion.

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

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,it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the entire population.

Instruction 8-14 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognise a new product. She samples 120 potential consumers and finds that 54 recognise this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54. -Referring to Instruction 8-14,95% of the time,the proportion of people that recognise the product will fall between 0.36 and 0.54.