Question

QUESTION: Using Microsoft^® Excel^®, run a chi square Goodness of Fit test to determine whether these observed starting salaries are significantly different. What do the findings tell you?

	Expected Salaries	Observed Salaries
Applicant 1	$20,000	$17,500
Applicant 2	$20,000	$20,000
Applicant 3	$20,000	$22,000
Applicant 4	$20,000	$20,500
Applicant 5	$20,000	$20,000

Answer 1

Hello Sir/Mam

Chi - square Goodness of Fit test using excel

Let the null hypothesis be that the actual salaries matches with expected salaries.

i.e. H₀ : X² = 0

	Expected Salaries	Observed Salaries	Formulas used
Applicant 1	20000	17500
Applicant 2	20000	20000
Applicant 3	20000	22000
Applicant 4	20000	20500
Applicant 5	20000	20000
p-value using chi-square goodness of fit test		2.6211E-112	=CHISQ.TEST(G8:G12,F8:F12)

The same value can also be found using:

	Expected Salaries	Observed Salaries	[(Observed-Expected)^2]/ Expected
Applicant 1	20000	17500	312.5
Applicant 2	20000	20000	0
Applicant 3	20000	22000	200
Applicant 4	20000	20500	12.5
Applicant 5	20000	20000	0
Total			525

Now, degree of freedomm = (n-1) = (5-1) = 4

Using, excel formula : "=CHISQ.DIST.RT(525,4)", we will find the same p-value, i.e. 2.6211E-112.

Now, Chi-Square Critical = CHISQ.INV.RT(0.05,4) = 9.4877

Now, p-value < , we can reject the null hypothesis and hence, we can say that the starting salaries are significantly different.

I hope this solves your doubt.

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