Exam 8: Confidence Interval Estimation

A university dean is interested in determining the proportion of students who receive some sort of financial aid.Rather than examine the records of all students,the dean randomly selects 200 students and finds that 118 of them are receiving financial aid.The 95% confidence interval for π is 0.59 ± 0.07.Interpret this interval.

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 ________.

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

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,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 of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option.Suppose there is no information about the proportion of students who might choose the option.What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $2,000.A random sample of 50 individuals resulted in an average income of $30,000.What is the upper end point in a 99% confidence interval for the average income?

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

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 critical value to use in obtaining the confidence interval is ________.

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,the parameter of interest is the proportion of student population who feel comfortable reporting cheating by their fellow students.

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 99% confidence interval for the mean voltage of the power packs is from ________ to ________.

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 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?

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.

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 approaches the standardised normal distribution when the number of degrees of freedom increases.

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

Suppose a 95% confidence interval for μ has been constructed.If it is decided to take a larger sample and to decrease the confidence level of the interval,then the resulting interval width would ________.(Assume that the sample statistics gathered would not change very much for the new sample. )

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 8-6,95% of all confidence intervals constructed similarly to this one will contain the mean of the population.

Instruction 8-9 A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburb of Sydney.His main concern is the total market value of the 3,605 houses in the suburb.From past experience,the standard deviation of market housing prices is estimated to be $81,000.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample average market price of $450,000 and a sample standard deviation of $77,400.The consulting group also found out that the average differences between market prices and appraised prices was $250,000 with a standard deviation of $6,800.Also the proportion of houses in the sample that are appraised for higher than the market prices is 0.24. -Referring to Instruction 8-9,what will be the 90% confidence interval for the total difference between the market prices and appraised prices of the houses in the suburb constructed by the consulting group?

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?

The sampling error can either be positive or negative.