Exam 8: Confidence Interval Estimation

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 goes from ________ to_________ .

Instruction 8-21 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 standardised test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. -Referring to Instruction 8-21,they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample S = 0.05,the critical value of t will be

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 8-1,95% of the stores have sold between 5.623 and 6.377 lawnmowers.

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 people will recognise the product between 36% and 54% of the time.

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,approximately how large a sample did her assistant use to determine the interval estimate?

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,the critical value for a 99% confidence interval for this sample is ____________.

Private colleges rely on money contributed by individuals for much of their major building expenses.Much of this money is put into a fund called a trust,and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in Australia revealed the following trusts (in millions of dollars): 60.2,47.0,235.1,490.0,122.6,177.5,95.4,and 220.0.Summary statistics yield $\bar { X }$ = 180.975 and S = 143.042.Calculate a 95% confidence interval for the mean trust of all the private colleges in Australia assuming a normal distribution for the trusts.

If an auditor believes that errors exist in a set of items and wants to estimate the magnitude of errors based only on a sample,the auditor will use the method of difference estimation.

Instruction 8-24 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 8-24,the report contains all the essential components for an ethical reporting of poll results.

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,it is possible that the 99% confidence interval calculated from the data will not contain the proportion of student population who own a personal computer.

The width of a confidence interval equals twice the sampling error.

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.Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

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

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 to use 25 days of data to construct the interval estimate,what confidence level can she attach to the interval estimate?

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,the mean of the sample is _________ ,while the standard deviation of the sample is _________ .

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 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

Instruction 8-13 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 8-13,suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence.Then the sample size would be________.

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.What is an efficient,unbiased point estimate of the number of books checked out each day at the National Library of Australia?