Exam 8: Confidence Interval Estimation

Instruction 8-7 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 8-7,the parameter of interest to the manager is the proportion of potential customers in this sample that recognise the new product.

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

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 critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report 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 total number of students in the population who feel comfortable reporting cheating by their fellow students.

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 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 8-12 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 90% 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 8-9 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 market price of the houses in the suburb constructed by the consulting group?

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 8-7 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 8-7,95% of the time,the proportion of people that recognise the product will fall between 0.36 and 0.54.

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,a 99% confidence interval for the mean of the population from the same sample would be wider than 27.5 to 30.3.

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.A preliminary sample indicates that the proportion will be around 0.25.Therefore,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?

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

The t distribution allows the calculation of confidence intervals for means when the actual standard error is not known.

Instruction 8-2 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 8-2,they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

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 size of the population is 1,500.

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

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?

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 width of the 90% confidence interval?

An officer with the Australian Electoral Office wants to estimate the proportion of retired voters who will need special election facilities.The officer wants to find a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion.How large a sample must be taken to assure these conditions are met?

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.