Question

Exercise 12. A researcher claims that the proportion of students that are pursuing a Bachelor of Arts degree and must work full time matches the distribution shown in the table on the left below. To test this claim, the researcher randomly surveyed 200 students, 50 from each year of study). The results are shown table on the right. At α = 0.05, is there evidence to support the researcher’s claim that the findings match the claimed distribution?

Researcher's Claim

CLASS Work full-time

Freshman 30%

Sophomore 32%

Junior 34%

Senior 38%

Researcher’s findings (n = 50 per class)

CLASS Work full-time

Freshman 14

Sophomore 18

Junior 17

Senior 21

Answer 1

We have to use goodness of fit chi-square test for testing whether the researcher's claims are consistent with the observed values.

There are 4 grades with 50 students in each class. To find out the expected number of full timers we will multiply 50 * (proportion of each grade).

Eg.: Freshman Ei = 50 * 0.30 = 15

Grade	Proportion assumed	Eepected Ei	Observed Oi	|Ei-Oi|
Freshman	0.3	15	14	1	1	0.066667
Sophomore	0.32	16	18	2	4	0.25
Junior	0.34	17	17	0	0	0
Senior	0.38	19	21	2	4	0.210526
Total						0.527193

The findings are consistent with the researcher's claim(distribution).

VS

The findings are not consistent with the researcher's claim(distribution).

Test Statistic:= 0.527193

Critical value: where 'k' is the number of categories

( can be found online from chi-square tables or using excel func 'chiinv' )

Decision Criteria: Reject null hypothesis if T.S. > C.V.

0.527193 < 9.3484

Decision: Since T.S. < C.V,we do not reject the null hypothesis at 5% level of significance.

Conclusion: The observed values matches with the researcher's claim. Hence,the distribution is a good fit.