Question

6) An economist is interested in studying the average income of consumers in a particular country. The population standard deviation of incomes is known to be $1,000.

What type of confidence interval should the economist build?

Group of answer choices

A t-based interval for the population mean.

No answer text provided.

A Z-based interval for the population proportion.

A Z-based interval for the population mean.

7) A race car driver tested his car for the time it takes to go from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. These times are known to be normally distributed.

What is the value of t used to construct a 95% confidence interval for the mean time it takes the car to go from 0 to 60? Round your answer to 2 decimal places.

8) A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet.A sample of 70 cut sheets yields a mean length of 12.14 feet and a sample standard deviation of 0.15 feet.

What type of confidence interval should the engineer build?

Group of answer choices

A Z-based interval for the population proportion.

A Z-based interval for the population mean.

A t-based interval for the population mean.

Answer 1

6) An economist is interested in studying the average income of consumers in a particular country. The population standard deviation of incomes is known to be $1,000.

What type of confidence interval should the economist build

As the parameter for which Confidence interval is being built is a population mean(the average income of consumers in a particular country) , and  Population standard deviation( of incomes )is known,

Type of confidence interval should the economist build is

Ans : A Z-based interval for the population mean

7) A race car driver tested his car for the time it takes to go from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. These times are known to be normally distributed

Formula for confidence interval for population mean when population standard deviation is not known

To find the value of t used 95% confidence interval for the mean time it takes the car to go from 0 to 60

for 95% confidence interval = (100-95)/100=0.05

/2 = 0.05/2=0.025

Sample size : n= 20

Value of t used 95% confidence interval for the mean time it takes the car to go from 0 to 60 = t_0.025,19

From standard t-tables,

Ans : t_0.025,19 = 2.093

8) A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet.A sample of 70 cut sheets yields a mean length of 12.14 feet and a sample standard deviation of 0.15 feet.

As Population standard deviation is not known , and the interested population parameter is a population mean (mean length of sheet insulation being cut automatically by machine)

Formula for confidence interval for population mean when population standard deviation is not known :

Hence,

type of confidence interval should the engineer build is

Ans : A t-based interval for the population mean