Every year a magazine lists the 500 best companies to work for, based on criteri
ID: 3330565 • Letter: E
Question
Every year a magazine lists the 500 best companies to work for, based on criteria such as pay, benefits, turnover rate, and diversity. Of the best 500 companies to workfor,181 experienced double digit job growth (10%-68%), 215 experienced single digit job growth (1%–9%), and104 experienced no growth or a decline. A closer examination of the top 100 showed that 36, had job growth in the double digits, 30 in the single digits, and only 34 had no growth or a decline. Is there anything unusual about job growth among the 100 top companies?
1) . Select the appropriate procedure. What kind of chi-square test would be appropriate?
Chi-square test for independence, Chi Square for goodness of fit, or chi square for homogeneity?
2)
Check the assumptions. Are all of the assumptions and conditions satisfied? Select all that apply.
A.
No, because the expected cell frequency condition is not satisfied.
B.
No, because the randomization condition is not satisfied.
C.
Yes, because all of the assumptions and conditions are satisfied.
D.
No, because the counted data condition is not satisfied.
3) State the hypotheses.
3) Test an appropriate hypothesis and state your results. Compute the appropriate X^2.
4) compute the p value if approrpiate.
5) Do you reject or fail to reject the hypothesis?
6) Interpret the meaning of the results and state your conclusion.
Explanation / Answer
1)Chi Square for goodness of fit, is used to see if top 100 companies follows the same level of job growth as experienced by best 500 companies
2)Yes, because all of the assumptions and conditions are satisfied
3) null hypothesis: Ho: top 100 companies follow the same distribution of job growth as by best 500 comapnies
alternate hypothesis:Ha: top 100 companies does not follow the same distribution of job growth as by best 500 comapnies
4) applying chi square goodness of fit test:
X2 test stat =12.8776
4) for above test ; degree of freedom =number of categories -1 =3-1=2
for 2 degree of fredom and above test stat ; p value=0.0016
5) as p value is very less we reject null hypothesis.
6)we have sufficient evidence to conclude that top 100 companies does not follow the same distribution of job growth as by best 500 comapnies
observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E double digt growth 181/500 42.000 27.15 8.12 single digit growth 215/500 21.000 32.25 3.92 no growth 104/500 12.000 15.60 0.83 1 75 75 12.8776Related Questions
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