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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 College students may be interested in whether or not their majors have any effect on starting-salaries after graduation. Suppose that 300recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Table 11.45shows the data. Conduct a test of independence.

Major<\(50,000
\)50,000-\(68,999\)69,000+
English5
205
Engineering10
3060
Nursing10
1515
Business10
20
30
Psychology20
3020

Table11.45

Short Answer

Expert verified

H0: Salaries are independent of majors

Takingα=0.05, we can see thatp<α. This means that we reject null hypothesis.

We can conclude that major and salary are not independent events.

Step by step solution

01

Given Information

Suppose that 300 recent graduates were surveyed as to their majors in college and their starting-salaries after graduation. Table 11.45 shows the data. Conduct a test of independence

02

Table with observed values

Table with observed values:

Major<$50,000$50,000-$68,999$69,000+Total
English5
20530
Engineering10
3060100
Nursing10
151540
Business10
20
3060
Psychology20
302070
Total55
115130300
03

Table with expected values

Table with expected values:

Major<$50,000
$50,000-$68,999$69,000+
Total
English5.511.513.030
Engineering18.3333338.3333343.33333100
Nursing7.33333315.33333317.333333
40
Business11232660
Psychology12.8333326.8333330.3333370
Total55115130300
04

Hypotheses test

We want to test these hypotheses:

H0 : Salaries are independent of majors

H1 : Salaries are dependent on majors

There are 5types of Major and 3groups of salaries. Thus, the number of degrees of freedom is

(51)(31)=42=8

We are usingχ2distribution. Our test statistic is given by:

χ2=i=15j=13(Obi,jExi,j)2Exi,j

=33.54553

05

Using the applet

Using the applet for theχ2distribution, we can find thatp-value is0.00005:

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Most popular questions from this chapter

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

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 the5%significance level, what can you conclude?

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’ survey indicate that the standard deviation is greater than 0.75?

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Table 11.42contains information from a survey among 499participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the USA. Perform a hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the USA obese population.

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20-30
22.4
122
31-40
18.6
104
41-50
12.8
78
51-60
10.4
64
61-70
35.8
168

Table11.42

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