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Chapter 8: Problem 38

Briefly explain the meaning of the degrees of freedom for a \(t\) distribution. Give one example.

Short Answer

Expert verified
Degrees of freedom in a t-distribution represents the number of values that are free to vary in the analysis. Its value influences the shape of the t-distribution. In a sample of size 30, for instance, the degrees of freedom would be 29, as one value is used to compute the mean, leaving 29 to vary freely.

Step by step solution

01

Understanding degrees of freedom

In statistics, degrees of freedom refer to the number of values in the final calculation of a statistic that are free to vary. In other words, the degrees of freedom can be defined as the number of independent observations which are used to compute a certain statistic.
02

Degrees of freedom in t-distribution

In a t-distribution, the degrees of freedom determine the shape of the distribution. As the degrees of freedom increase, the t-distribution approaches the shape of the normal distribution. When the sample size(s) increase in a particular sample, the degrees of freedom also increase, making the distribution more similar to a standard normal distribution.
03

Example application of degrees of freedom

Suppose we are testing a hypothesis using a sample of size 30. The degrees of freedom in this case would be 30-1=29. This is because one degree of freedom is consumed in calculating the sample mean. The remaining 29 are free to vary.

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Most popular questions from this chapter

According to the 2010 Time Use Survey conducted by the U.S. Bureau of Labor Statistics, Americans of age 15 years and older spent an average of 164 minutes per day watching TV in 2010 (USA TODAY, June 23,2011 ). Suppose a recent sample of 25 people of age 15 years and older selected from a city showed that they spend an average of 172 minutes per day watching TV with a standard deviation of 28 minutes. Make a \(90 \%\) confidence interval for the average time that all people of age 15 years and older in this city spend per day watching TV. Assume that the times spent by all people of age 15 years and older in this city watching TV have a normal distribution.

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