College students may be interested in whether or not their majors have any effec

Question

College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 300 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test for independence at the 5% level.

Part (a)

State the null hypothesis. Choose 1 or 2

1. An individual's starting salary after graduation is independent of that individual's major in college.

2. An individual's starting salary after graduation is dependent on that individual's major in college.   

State the alternative hypothesis. Choose 1 or 2

1. An individual's starting salary after graduation is independent of that individual's major in college.

2. An individual's starting salary after graduation is dependent on that individual's major in college.    

Part (b)

What are the degrees of freedom? _______

Part (c)

State the distribution to use for the test. Choose 1, 2, 3, 4

1. t8

4. t4

Part (d)

What is the test statistic? (Round your answer to two decimal places.) _________

What is the p-value? (Round your answer to four decimal places.) ________

Part (e)
Explain what the p-value means for this problem. Choose

1. H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

2. H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.   

3. H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

4.H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

Major < $30,000 $30,000 - $39,999 $40,000 + English 5 21 4 Engineering 11 30 59 Nursing 9 15 15 Business 10 21 30 Psychology 20 29 21

Explanation / Answer

The statistical software output for this problem is:

Contingency table results:
Rows: Major
Columns: None

Chi-Square test:

Hence,

a) Null hypothesis: Option 1 is correct.

Alternative hypothesis: Option 2 is correct.

b) Degrees of freedom = 8

c) Option 3 is correct.

d) Test statistic = 33.14

P-value = 0.0000

e) Option 2 is correct.

< $30,000 $30,000 - $39,999 $40,000 + Total English 5 21 4 30 Engineering 11 30 59 100 Nursing 9 15 15 39 Business 10 21 30 61 Psychology 20 29 21 70 Total 55 116 129 300

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