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211-01-02+Class+23+hw16 - HW16 solution guide Ex 12-13(p...

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HW16 solution guide Ex 12-13 (p 490) Issue: Health Insurance Coverage by Employers Ques: Does the distribution of health insurance coverage differ by size of company? -- All US companies. Data: Definitions: small = '> 100 employees', medium = '100-999 employees', and large = '1000 or more employees.' (evidence) Sample of employees from all three size firms -- recorded whether covered or not by health insurance. Health Insurance Total Since row totals Samp Proportions Total Small Medium Large Yes No are different, Yes No Yes Yes No Small 36 14 50 could show Small 0.72 0.28 1.00 No Yes Yes Medium 65 10 75 proportions of yes Medium 0.87 0.13 1.00 Yes Yes Yes Large 88 12 100 & no for ea row. Large 0.88 0.12 1.00 Yes No Yes Total: 189 36 225 Total: 0.84 0.16 1.00 No Yes This helps in interpretation. Yes Yes Analysis: ChiSQ Test of Independence: No 1. Hyp's: Ho: Distributions of health care coverage are the same of all three size companies. Yes Ha: Distributions are not all the same. 2. TeStat: (1) ChiSq = Sum of (e-f)^2/e for all the 6 cells of the contingency table. f = observed frequencies (2) If Ho is true, this statistic is ChiSq distributed with df = (3-1)*(2-1) = 2 e = expected if Ho were true 3. SigLev: alpha = 0.05 4. RejRule Reject Ho if ChiSq > 5.991 =CHIINV(.05,2) 5. Calculations: Expecteds - if Ho were true: e's: Health Insurance Total Note. All e's are >=5. Yes No Small 42 8 50 Medium 63 12 75 Large 84 16 100 Total: 189 36 225 (e-f)^2/e Health Insurance Total Yes No Small 0.857 4.500 5.357 Medium 0.063 0.333 0.397 Large 0.190 1.000 1.190 Total: 1.111 5.833 6.944 =ChiSq p-value = 0.031 =CHIDIST(6.944,2) 6. Concl: Reject Ho. Answer: health care coverage is NOT independent of size of company. We can conclude that the proportion of small companies providing coverage is smaller than that proportion of medium and large companies. For the sample, 72% of small and 87/88% of med/large companies provided health coverage. NOTE: Sample results could have come as follows. Sample Results (f's): Company size Company size We'd use =countif to find the sample results of the 1st table. Company size Company size From this sample of 225 companies, there is strong evidence to conclude that
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Prob 1. Exercise 20 (page 532) Name Small* Name Medium* Name Large* Small* Medium* Large* Issue: Cruise Ships & Service Ratings Hanseactic 90.5 Amsterdam 91.1 Century 89.2 90.5 91.1 89.2 BusQues: Are there differences in the mean service ratings of the three sizes of cruise ships? Mississippi Queen 78.2 Crystal Symphony 98.9 Disney Wonder 90.2 78.2 98.9 90.2 (If so, what are they? Compare the different sizes with each other.) Philae 92.3 Maasdam 94.2 Enchantment of the Seas 85.9 92.3 94.2 85.9 Data: Samples of eight randomly selected small, medium, and large cruise ships: Royal Clipper 95.7 Noordam 84.3 Grand Princess 84.2 95.7 84.3 84.2 service ratings for each (100 point scale with higher values indicated better service. Seabourn Pride 94.1 Royal Princess 84.8 Infinity 90.2 94.1 84.8 90.2 See columns J - O. Seabourn Spirit 100 Ryndam 89.2 Legend of the Seas 80.6 100 89.2 80.6 Analysis: ANOVA Silver Cloud 91.8 Statendam 86.4 Paradise 75.8 91.8 86.4 75.8 1. Hyp: Silver Wind 95 Veendam 88.3 Sun Princess 82.3 95 88.3 82.3 Ha: Not all the same. of each size, S, M, & L.
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