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

The number of degrees of freedom for a test of independence is equal to the sample size minus one.

Short Answer

Expert verified

The statement is false.

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

If we are given the table with nrow and mcolumns, the number of degrees of freedom is calculated as

(n-1)(m-1)

Thus, the statement is false.

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Most popular questions from this chapter

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

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:

Industry Sector200020102020TotalNonagriculture wage and salary13,24313,04415,01841,305Goods-producing, excluding agriculture2,4571,7711,9506,178Services-providing10,78611,27313,06835,127Agriculture, forestry, fishing, and hunting240214201655Nonagriculture self-employed and unpaid family worker9318949722,797Secondary wage and salary jobs in agriculture and private householdindustries14111136Secondary jobs as a self-employed or unpaid family worker196144152492Total27,86727,35131,37286,590

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 .

Letฮฑ=0.05

Decision: ________

Conclusion (write out in a complete sentence.): ________

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.

An ice cream maker performs a nationwide survey about favorite flavors of ice cream in different geographic areas of the U.S. Based on the Table, do the numbers suggest that geographic location is independent of favorite ice cream flavors? Test at the 5%significance level.

USRegionStraChocoVanRockyRoadMintChocolateChipPistachioTotalWest1221221915897Midwest1032221115696East83127815796South1528308156102Total45112101466027391
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