Confidence Interval and Margin of Error

Researchers want to estimate with 95% confidence the true mean pulse rate of American adult males who jog at least 15 miles per week. They survey 21 males and find the sample mean pulse rate to be 52.6 beats per minute and a standard deviation of 3.22 beats per minute. Find the margin of error for the mean pulse rate of all American adult males who jog at least 15 miles per week. Round to the nearest tenth.

• 1.4 beats per minute

• 1.7 beats per minute

• 0.9 beats per minute

• 4.1 beats per minute

Researchers want to estimate with 95% confidence the true mean pulse rate of American adult males who jog at least 15 miles per week. They survey 21 males and find the sample mean pulse rate to be 52.6 beats per minute and a standard deviation of 3.22 beats per minute. Suppose the researchers want to estimate the mean within 1 beat per minute. How large must the sample size be? Round to the nearest whole number.

• 41

• 21

• 53

• 36

The operations manager of a large production plant wants to estimate the mean amount of time a worker takes to assemble a new electric component. Assume the standard deviation of the assembly time is 3.6 minutes. After observing 120 workers, the manager found their mean assembly time to be 16.2 minutes. Construct a 95% confidence interval for the estimate of the mean assembly time. Round to the nearest hundredth.

• [15.54, 16.86]

• [13.24, 19.16]

• [14.41, 17.99]

• [10.94, 21.46]

The operations manager of a large production plant wants to estimate the mean amount of time a worker takes to assemble a new electric component. Assume the standard deviation of the assembly time is 3.6 minutes. How many workers should be observed if the manager wants to estimate the mean assembly time within 0.25 minutes? Round to the nearest whole number.

• 829

• 29

• 415

• 58

Complete the following statement about the change in size. If you increase the size of your sample, the ME will . . . .

• increase

• decrease

• stay the same

Complete the following statement about the change in size. If your sample has a larger standard deviation, the ME will . . . .

• increase

• decrease

• stay the same

A sample size of n = 64 is drawn from a population whose standard deviation is σ = 5.6.

Find the margin of error for a 99% confidence interval for µ.

• 1.799

• 1.798

• 1.803

An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.

Find the Margin of Error to two decimal places.

• 1.90

• 1.89

• 1.899

• 1.99

A population has a standard deviation of σ = 17.3. How large of a sample must be drawn so that a 95% confidence interval for µ will have a Margin of Error equal to 1.4?

• 586.6

• 587

• 586

• 585

A large sample has mean of 7.1 and Standard Error of 2.3.

Construct a 90% Confidence Interval for the population mean µ (to two decimal places).

• (3.32, 10.88)

• (3.8, 7.1)

• (3.3, 10.9)

• (3.3165, 10.8835)