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Read the statement and decide whether it is true or false.

The test for independence uses tables of observed and expected data values.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Concept Introduction

The Chi-square test of independence is a statistical hypothesis test used to determine whether two categorical or nominal variables are likely to be related or not.

02

Explanation

The test statistic of the independence test is given below:

Teststatistic=(i×j)(O-E)2E

Here, Ois observed value and Eis expected value.

Therefore, it can say that the test for independence uses tables of observed and expected data values. Hence, the statement is true.

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Most popular questions from this chapter

Decide whether the following statements are true or false;

The standard deviation of the chi-square distribution is twice the mean.

A sample of 212commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. Table 11.41shows 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 commodityExpected number that recycles one commodity
office35
19
17.5
Retail/
Wholesale
48
27
24
Food/
Restaurants
53
35
26.5
Manufacturing/
Medical
52
21
26
Hotel/Mixed24
9
12

Table 11.41

Conduct a goodness-of-fit test to determine if the actual college majors of graduating males fit the distribution of their expected majors.

MajorMen - Expected MajorMen - Actual MajorArts & Humanities11.0%600Biological Sciences6.7%330Business22.7%1130Education5.8%305Engineering15.6%800Physical Sciences3.6%175Professional9.3%460Social Sciences7.6%370Technical1.8%90Other8.2%400Undecided6.6%340

A plant manager is concerned her equipment may need recalibrating. It seems that the actual weight of the 15oz. cereal boxes it fills have been fluctuating. The standard deviation should be at most 0.5oz. In order to determine if the machine needs to be recalibrated, 84randomly selected boxes of cereal from the next day’s production were weighed. The standard deviation of the 84 boxes was 0.54. Does the machine need to be recalibrated?

A factory manager needs to understand how many products are defective versus how many are produced. The number of expected defects is listed in Table 11.5.

Number producedNumber defective0-1005101-2006201-3007301-4008401-50010

A random sample was taken to determine the actual number of defects. Table 11.6 shows the results of the survey.

Number producedNumber defective0-1005101-2007201-3008301-4009401-50011

State the null and alternative hypotheses needed to conduct a goodness-of-fit test, and state the degrees of freedom.

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