Math Margin of Error

A high school randomly selected 75 of the 200 seniors at the school to take a sample college entrance exam. The mean grade point average (GPA) of the seniors selected was 2.85, and the standard deviation was 0.4. Select all the statements that are true. (Note: Margin of error ≈2\frac{s}{\sqrt{n}} where s is the standard deviation and n is the sample size.)

• The margin of error for the mean grade point average is about 0.057

• The margin of error for the mean grade point average is about 0.092

• The margin of error would decrease if the sample size were changed to 125 seniors. 

• The margin of error would increase if the sample size were changed to 125 senior. 

The police chief of a town is trying to determine the average speed of drivers on a specific road. The police chief took a random sample of the speeds of 100 drivers on the road. The mean was 48.5 miles per hour, with a standard deviation of 2.5 miles per hour. The police chief wanted to decrease the margin of error of his next sample. Which would decrease the margin of error?

• decreasing the sample size

• increasing the sample size

• changing the time that the data is collected

• changing the road on which the data is collected

A company makes and boxes spaghetti. One machine fills each box with about 32 ounces of spaghetti. After the boxes are filled, another machine weighs each box. A box is discarded if the weight of the box differs by more than 0.25 ounce from the target weight of 32 ounces. Which inequality can be used to find the range of acceptable weights, x, of the spaghetti?

For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220. Find the margin of error for the sample mean. (assuming 95% confidence) Round to the nearest hundredth

• $77.78

• $4.31

• $188.78

• $494.97

At the Greenville County Cross Country Championships, a college scout took a sample of 20 runners. The average time was 17.25 minutes with a standard deviation of .03. Find the Margin of Error with 99% Confidence.

Identify the variables for the Margin of Error formula

• 20

• Z

• 2.58

• n

• .03

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

A sports analyst for an NBA team surveyed 50 games. The average points per game was 113 with a standard deviation of 5.6. Find the Margin of Error with 90% Confidence.

Identify the variables used in the Margin of Error formula

• 1.645

• 50

• n

• 5.6

• Z

Margin of error equals:

• Critical Value ∗ standard Error

• z*

• 1.96

• Standard Error

What can you do to reduce the margin of error? 

• increase sample size

• decrease sample size

How could Javier decrease the margin of error?

• Increase the sample size

• Decrease the sample size