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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.39 (page 657)

Is this a right-tailed, left-tailed, or two-tailed test? Explain why.

Short Answer

Expert verified

It is a right-tailed test.

Step by step solution

Given Information

Given data:

Explanation

The test of independence is always a right-tailed test, depending on how the test statistic is calculated.

We can assume that because observed values are not close together, big test statistics will result, and this test statistic will fall on the right tail of the chi-square curve, as it does in a goodness-of-fit test.

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Most popular questions from this chapter

In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.

A sample of $212$ commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. Table $11.41$ shows the business categories in the survey, the sample size of each category, and the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the $5$ % significance level, perform a hypothesis test to determine if the observed number of businesses that recycle one commodity follows the uniform distribution of the expected values.

Business Type	Number in class	Observed Number that recycles one commodity	Expected number that recycles one commodity
office	$35$	$19$	$17.5$
Retail/ Wholesale	$48$	$27$	$24$
Food/ Restaurants	$53$	$35$	$26.5$
Manufacturing/ Medical	$52$	$21$	$26$
Hotel/Mixed	$24$	$9$	$12$

Table 11.41

Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of $200$ passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

$\begin{array}{l} Traveling Distance & Third class & Second class & First class & Total \\ 1 - 100 miles & 21 & 14 & 6 & 41 \\ 101 - 200 miles & 18 & 16 & 8 & 42 \\ 201 - 300 miles & 16 & 17 & 15 & 48 \\ 301 - 400 miles & 12.00 % & 14 & 21 & 47 \\ 401 - 500 miles & 6 & 6 & 10 & 22 \\ Total & 73 & 67 & 60 & 200 \end{array}$

State the hypothesis:

$H_{0}$ :

$H_{α}$ :

Is it more likely the $d f i s 90, 20, o r 2$ in the graph?

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

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Is this a right-tailed, left-tailed, or two-tailed test? Explain why.

Short Answer

Step by step solution

Given Information

Explanation

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