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 8-7,95% of the people will recognise the product between 36% and 54% of the time.

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 is 54/120 = 0.45.

In estimating the population mean with the population standard deviation unknown,if the sample size is 12,there will be 6 degrees of freedom.

A population parameter is used to estimate a confidence interval.

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

Sampling error equals to half the width of a confidence interval.

Instruction 8-10 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 8-10,the sampling error of a 99% confidence interval for the proportion of student population who own a personal computer is ________.

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 8-2 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,this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

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.

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 confidence interval for this sample would be based on the t distribution with ________ degrees of freedom.

Instruction 8-10 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 8-10,a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who own a personal computer is normal.

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.

The confidence interval obtained will always correctly estimate the population parameter.

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 sample.

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 confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

Instruction 8-8 A hotel chain wants to estimate the average number of rooms rented daily in each month.The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 24 rooms. -Referring to Instruction 8-8,during January,a sample of 16 days has a sample mean of 48 rooms.This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms.What is the level of confidence of this interval?

An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $1,000.A random sample of 50 individuals resulted in an average income of $30,000.What sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

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 the time,the sample mean salary offer to students majoring in management will fall between 27.5 and 30.3.

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,we do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.