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# Sampling Distributions and the t-Distribution Practice Questions

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Updated on Oct 5, 2011

To review these concepts, go to Sampling Distributions and the t-Distribution Study Guide.

## Sampling Distributions and the t-Distribution Practice Questions

### Practice

For each of the following circumstances, explain whether the quantity in bold is a parameter or a statistic.

1. The Department of Transportation used a radar gun to measure the speed of a random sample of vehicles driving on a specific five-mile stretch of interstate from 8:00 to 8:30 A.M. The average speed of these vehicles was 63 miles per hour.
2. The average age of all residents at a nursing home is 85.

For each of the following, specify whether or μ is the correct statistical notation for each mean described.

1. The mean salary of teachers at a high school is \$35,000 a year.
2. For a random sample of 35 college students, the average time per week they spent studying was 7.8 hours.

In a large retirement community, the age of residents is normally distributed with mean 73 years and standard deviation 13 years. Consider randomly selected samples of size n = 75 residents.

1. What is the mean of the sampling distribution of the sample means?
2. What is the standard deviation of the sampling distribution of the sample means?
3. Use properties of the normal distribution to fill in the blanks in the following sentence: "For 95% of all randomly selected samples of size n = 75 residents, the mean age will be between ___and ___ years."
1. Find t* such that P(t >t*) = 0.01 when t has 27 degrees of freedom.
2. Find t* such that P(|t| > t*) = 0.01 when t has 23 degrees of freedom.
3. Find t* such that P(t < t*) = 0.01 when t has 20 degrees of freedom.

#### Solutions

1. Statistic
2. Parameter
3. μ
4. 73 years
5. 1.5 years
6. For 95% of all randomly selected samples of size n = 75 residents, the mean age will be between 70 and 76 years.
7. t* = 2.473
8. t* = 2.807
9. t* = –2.528

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