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Suppose that 600thirty-year-olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test of independence

AnnualSalaryNot a high schoolgraduateHigh schoolgraduateCollegegraduateMasters ordoctorate<\(30,0001525105\)30,000-\(40,00020407030\)40,000-\(50,00010204055\)50,000-\(60,0005102060\)60,000+0510150

Short Answer

Expert verified

Decision: Reject the null hypothesis H0

Conclusion: There is sufficient evidence to ensure that the salary is dependent on the level of education an individual has.

Step by step solution

01

Given Information

The null hypothesis is shown below:

H0: The salary is independent of the level of education an individual has.

Against the alternative hypothesis as shown below:

Ha: The salary is dependent of the level of education an individual has.

02

Degrees of freedom

The degrees of freedom can be calculated by the formula given below:

df=(numberofcolumns-1)(numberofrows-1)

Therefore,

df=(numberofcolumns-1)(numberofrows-1)

=(4-1)(5-1)

=34

=12

From the above calculation, it is clear that the distribution for the test is 122.

03

Tables

The observed value table is already given in the textbook. Calculate the expected frequencies by using the formula shown below:

E=(row total)(column total)overall total

All calculations can be done in excel worksheet. Hence, the expected(E)values table is shown below:

The test statistic of independence test is given below:

Teststatistic=(ij)(O-E)2E

To calculate (O-E)2Eapply formula =(B4-B14)2/B14in cell B21 and drag the same formula up to cell F24. After that, take total of columns total and rows total. The table of the test statistic is shown below:

Hence, the test statistic is 255.77.

The p-value can be calculated in excel by using CHIDIST ( ) formula as shown below:

Hence, thep- value is0.000

04

Graph

Chi-square sketch is given below:

05

Decision, Reason and conclusion

Alpha:0.05

Decision: Reject the null hypothesis H0

Reason for decision: Becausep-value<

Conclusion: There is sufficient evidence to ensure that the salary is dependent of the level of education an individual has.

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Most popular questions from this chapter

The number of births per woman in China is 1.6down from 5.91in 1966. This fertility rate has been attributed to the law passed in 1979restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50women across China the number of births they had had. The results are shown in Table. Does the students鈥 survey indicate that the standard deviation is greater than 0.75?

# of birthsFrequency0513021035

A 2013poll in California surveyed people about taxing sugar-sweetened beverages. The results are presented in the Table and are classified by ethnic group and response type. Are the poll responses independent of the participants鈥 ethnic group? Conduct a test of independence at the 5%significance level.

OpinionlEthnicityAsian-AmericanWhite/Non-HispanicAfrican-AmericanLatinoRowTotalAgainst tax4843341160682In Favor of tax5423424147459No opinion1643161994Column Total118710813261235

Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place are shown in Table. Conduct a test for homogeneity at a 5%level of significance.

French ToastPancakesWafflesOmelettesMen47352853Women65595560

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.

A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 643members of the sports club are randomly selected. Conduct a test of independence.

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The expected percentage of the number of pets students have in their homes is distributed (this is the given distribution for the student population of the United States) as in Table 11.12.

Number of PetsPercent0181252303184+9

A random sample of 1,000students from the Eastern United States resulted in the data in Table 11.13.

Number of PetsFrequency02101240232031404+90

At the 1% significance level, does it appear that the distribution 鈥渘umber of pets鈥 of students in the Eastern United States is different from the distribution for the United States student population as a whole? What is the p-value?

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