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 298 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test of independence. (Use a significance level of 0.05.)

Part (a)

State the null hypothesis.

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

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

Part (b)

State the alternative hypothesis.

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

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

Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

Part (d)

State the distribution to use for the test.

28

24

t8

t4

Part (e)

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

Part (f)

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


Explain what the p-value means for this problem.

If 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.

If 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.   

If 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.

If 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.

Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)

=  

(ii) Decision:

reject the null hypothesis

do not reject the null hypothesis    

(iii) Reason for decision:

Since > p-value, we reject the null hypothesis.Since > p-value, we do not reject the null hypothesis.   

Since < p-value, we do not reject the null hypothesis.Since < p-value, we reject the null hypothesis.

(iv) Conclusion:

There is sufficient evidence to conclude that an individual's starting salary after graduation is dependent on that individual's major in college.

There is not sufficient evidence to conclude that an individual's starting salary after graduation is dependent on that individual's major in college.   

Major < $50,000 $50,000 - $68,999 $69,000 + English 5 19 4 Engineering 10 29 61 Nursing 9 16 14 Business 11 19 31 Psychology 20 31 19 p-value

Explanation / Answer

null:An individual's starting salary after graduation is independent of that individual's major in college

alternate: An individual's starting salary after graduation is dependent of that individual's major in college.

c) degrees of freedom =(row-1)*(column-1) =(5-1)*(3-1) =8

d)28

e)

applying chi square test:

test statistic =36.6139

f) p value =0.0000

g)bottom left curve is correct

h) = 0.05

(ii) Decision:

reject the null hypothesis

(iii) Reason for decision:

Since > p-value, we reject the null hypothesis

(iv) Conclusion:

There is sufficient evidence to conclude that an individual's starting salary after graduation is dependent on that individual's major in college.

Observed O < $50,000 $50,000 - $68,999 $69,000 + Total English 5 19 4 28 Engineering 10 29 61 100 Nursing 9 16 14 39 Business 11 19 31 61 Psychology 20 31 19 70 Total 55 114 129 298 Expected E=rowtotal*column total/grand total < $50,000 $50,000 - $68,999 $69,000 + Total English 5.168 10.711 12.121 28 Engineering 18.456 38.255 43.289 100 Nursing 7.198 14.919 16.883 39 Business 11.258 23.336 26.406 61 Psychology 12.919 26.779 30.302 70 Total 55 114 129 298 chi square =(O-E)^2/E < $50,000 $50,000 - $68,999 $69,000 + Total English 0.0054 6.4138 5.4408 11.860 Engineering 3.8746 2.2391 7.2466 13.360 Nursing 0.4511 0.0783 0.4922 1.022 Business 0.0059 0.8055 0.7992 1.611 Psychology 3.8805 0.6655 4.2154 8.761 Total 8.218 10.202 18.194 36.6139

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