Question

The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). We are testing the claim that the starting salaries for new college graduate are different depending on the positions at α=0.2α=0.2 given the following data

Group 1: Internship	Group 2: Co-op	Group 3: Work Study
10	11.25	16
14.75	13	14
10.5	13.5	14
9.5	17.75	13
14.75	8.5	16.5
14	10	16
15	14	13.5
11	14.25	12
12.75	12.5	15.75
11.25	13.25	16.25

1. For this study, we should use Select an answer χ²GOF-Test T-Test 1-PropZInt TInterval 2-PropZInt 2-SampTInt χ²-Test ANOVA 1-PropZTest 2-SampTTest 2-PropZTest
2. 
   
3. Your friend Monique helped you with the null and alternative hypotheses...
   H0: μ1=μ2=μ3H0: μ1=μ2=μ3
   H1:H1: At least one of the mean is different from the others.
   
4. The test-statistic for this data = (Please show your answer to 3 decimal places.)
5. 
   
6. The p-value for this sample =  (Please show your answer to 4 decimal places.)
7. 
   
8. The p-value is Select an answer greater than alpha, less than (or equal to) alpha  αα
9. 
   
10. Base on this, we should Select an answer accept the null hypothesis, reject the null hypothesis, accept the alternative hypothesis fail to reject the null hypothesis  hypothesis
11. 
    
12. As such, the final conclusion is that...
    • Base on the sample data, there is sufficient evidence to conclude the claim that the starting salaries for new college graduate are different depending on the positions at αα = 0.2.
    • Base on the sample data, there is not sufficient evidence to conclude the claim that the starting salaries for new college graduate are different depending on the positions at αα = 0.2.

Answer 1

Ans:

We should use ANOVA.

Test statistic,F=3.447

p-value=0.0464

(calculations for ANOVA is done in below given tables)

The p-value is less than (or equal to) alpha  α.

we should reject the null hypothesis.

Base on the sample data, there is sufficient evidence to conclude the claim that the starting salaries for new college graduate are different depending on the positions at α = 0.2.

	Group 1	Group 2	Group 3	Total
Sum	123.5	128	147	398.5
Count	10	10	10	30
Mean, Sum/n	12.35	12.8	14.7
Sum of square, Ʃ(xᵢ-x̅)²	41.525	57.6	22.725
Standard deviation	2.148	2.530	1.589

Number of treatment, k =	3
Total sample Size, N =	30
df(between) = k-1 =	2
df(within) = N-k =	27
df(total) = N-1 =	29
SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N =	31.117
SS(within) = SS1 + SS2 + SS3 =	121.850
SS(total) = SS(between) + SS(within) =	152.967
MS(between) = SS(between)/df(between) =	15.558
MS(within) = SS(within)/df(within) =	4.513
F = MS(between)/MS(within) =	3.447
p-value = F.DIST.RT(3.4475, 2, 27) =	0.0464

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	31.1167	2	15.5583	3.447	0.0464
Within Groups	121.8500	27	4.5130
Total	152.9667	29