Exam 8: Confidence Interval Estimation

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

The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

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,if the population had consisted of 10,000 stores,the confidence interval estimate of the mean would have been wider in range.

Instruction 8-18 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 8-18,what is the needed sample size to obtain a 95% 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?

A confidence interval was used to estimate the proportion of business statistics students that are females.A random sample of 72 business statistics students generated the following 90% confidence interval: (0.438,0.642).Using the information above,what total sample size would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence?

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,the parameter of interest to the manager is the proportion of potential customers in this sample that recognise the new product.

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.Which of the following assumptions is necessary in order for a confidence interval to be valid?

When estimating the rate of non-compliance,it is commonplace to use a ________ 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,we are 95% confident that the population mean number of managers who have caught employees cheating on an expense report is between 0.5116 to 0.6484.

The width of a confidence interval estimate for a proportion will be

Instruction 8-6 A sample of salary offers (in thousands of dollars) given to students majoring in management is: 28, 31, 26, 32, 27, 28, 27, 30, 31, and 29. Using this data to obtain a 95% confidence interval resulted in an interval from 27.5 to 30.3. -Referring to Instruction 8-6,it is possible that the mean of the population is between 27.5 and 30.3.

The head librarian at the National Library of Australia has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant provides the following interval estimate: from 740 to 920 books per day.If the head librarian knows that the population standard deviation is 150 books checked out per day,and she asked her assistant for a 95% confidence interval,approximately how large a sample did her assistant use to determine the interval estimate?

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 sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is ________.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).Give a definition of what it means to be "95% confident" in an inference.

Other things being equal,the confidence interval for the mean will be wider for 95% confidence than for 90% confidence.

Instruction 8-16 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 8-16,a 99% confidence interval will contain 99% of the student population who own a personal computer.

The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store.Fifteen credit card accounts were randomly sampled and analysed with the following results: $\bar { X }$ = $50.50 and S = 20. -Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution.

Instruction 8-16 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 8-16,we are 99% confident that the average numbers of student population who own a personal computer is between 0.7911 and 0.8769.

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