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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 902 pages

ISBN: 9781938168208

Chapter 11: Q.64 (page 658)

The standard deviation of heights for students in a school is $0.81$ . A random sample of $50$ students is taken, and the standard deviation of heights of the sample is $0.96$ . A researcher in charge of the study believes the standard deviation of heights for the school is greater than $0.81$ .
To find the value of $d f$ .

Short Answer

Expert verified

The number of degrees of freedom is $d f = 49$ .

Step by step solution

01

Given Information

A random sample of $50$ students is taken, and the standard deviation of the heights of the sample is $0.96$ .

02

Explanation

We have to find the value of degrees of freedom:

A random sample has $n = 50$ students.

Therefore, the number of degrees is :

$n - 1$

$= 50 - 1$

$= 49$

The value of degrees of freedom is $d f = 49$

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Most popular questions from this chapter

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

How did you know to test the variance instead of the mean?

A teacher predict that the distribution of grades on the final exam will be and they are recorded in table 11.27

The actual distribution for a class of 20 is in table 11.28

At the $5 %$ significance level, what can you conclude?

The Bureau of Labor Statistics gathers data about employment in the United States. A sample is taken to calculate the number of U.S. citizens working in one of several industry sectors over time. Table 11.17 shows the results:

$\begin{array}{l} Industry Sector & 2000 & 2010 & 2020 & Total \\ Nonagriculture wage and salary & 13, 243 & 13, 044 & 15, 018 & 41, 305 \\ Goods-producing, excluding agriculture & 2, 457 & 1, 771 & 1, 950 & 6, 178 \\ Services-providing & 10, 786 & 11, 273 & 13, 068 & 35, 127 \\ Agriculture, forestry, fishing, and hunting & 240 & 214 & 201 & 655 \\ Nonagriculture self-employed and unpaid family worker & 931 & 894 & 972 & 2, 797 \\ \begin{array}{l} Secondary wage and salary jobs in agriculture and private household \\ industries \end{array} & 14 & 11 & 11 & 36 \\ Secondary jobs as a self-employed or unpaid family worker & 196 & 144 & 152 & 492 \\ T o t a l & 27, 867 & 27, 351 & 31, 372 & 86, 590 \end{array}$

We want to know if the change in the number of jobs is independent of the change in years. State the null and alternative hypotheses and the degrees of freedom .

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Perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population, based on ethnicity.

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