Math 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. 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 your sample has a larger standard deviation, the ME will . . . .

• increase

• decrease

• stay the same

A research team surveys 1001 adults, asking them how many hours they work per week. What is the margin of error for this survey?

• 3%

• 32%

• 63%

• 9%

A recent survey found that out of 400 random American adults, 89% pay their bills on time. The margin of error in this survey was 2%. What is the interval of values in which the truth is likely found?

• 89% - 91%

• 87% - 89%

• 87% - 91%

• 388 - 402

A recent survey found that 77% of high schoolers use their phones more than 4 hours a day on average. The margin of error was 3%. What is the interval for which we could expect to find the truth of the population?

• 77% - 80%

• 74% - 77%

• 74% - 80%

• 50 million high schoolers - 120 million

A recent survey of 2000 high schoolers found that 80% use their phones more than 4 hours a day on average. What is the interval for which we could expect to find the truth of the population?

• 2%

• 78% - 82%

• 93% - 97%

• 82%

A random sample of shoppers chose between two similar products, and the percent who chose Brand A was recorded. The table shows the results of 20 simulations. Based on the simulations, which of the following is the most likely margin of error for the sample?

• ±1

• ±2.5

• ±8

• ±16

The results of a survey suggested that 54% of the voters will vote for a particular candidate in an election. The results from 100 computer simulations of this situation are shown below. Based on the margin of error and these simulations, what is the range of the percentages of votes this candidate could receive?

• 0.45 to 0.63

• 0.48 to 0.58

• 0.54 to 0.74

• 0.59 to 0.69