211-01-02+Class+17+HW12_1_

211-01-02+Class+17+HW12_1_ - HW 12 Ex 35 (p 439) Issue:...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW 12 Ex 35 (p 439) Issue: Quality of two TV commercials BusQues: Can we conclude that there is a difference in the "recall proportions" for the two commercials? (If so, which is a stronger commercial?) Data: Telephone surveys after commercials shown 6 times in one week. p-barA = 0.420 sample recall proportion --A (evidence) Sample of 150 individuals vis-à-vis commerical A; 63 recalled it. Sample of 200 individuals vis-à-vis commercial B: 60 recalled it. p-barB = 0.300 sample recall proportion --B p-bar = pooled est of p = 0.351 =(150*0.42 + 200*0.30)/(150+200) Analysis: Normal Test for Two Proportions [need because Ho includes equality] 1 Ho: pA = pB, or pA-pB = 0 Ha: pA <> pB, or pA-pB <> 0 2 Test statistic: (1) p-barA - pbarB, (difference in the sample proportions) (2) If Ho is true, this statistic is Normal with mean = 0 and std err we can calculate. Std Error = 0.052 =(p-bar*(1-p-bar)*(1/150+1/200))^.5 3 Sig Level: alpha = 0.05 4 Reject rule: 5 Calculations: 6 Conclusion: BusAnswer: Reject Ho if (p-barA-p-barB) < -0.101 or > =NORMINV(.025,0,0.052) p-barA-p-barB = p-value = Reject Ho 0.120 0.020 <-- Need to use "pooled" p-bar 0.101 =NORMINV(0.975,0,0.052) =1-NORMDIST(0.12,0,0.052,TRUE) The data of these two samples provide strong evidence to conclude that the recall proportion for commercial A is higher than that for commercial B. For these samples, the recall is 12 % higher for commercial A than B. Sample Recall proportion (A) = 0.42, i.e. 42% of the sample of 150 recalled commercial A. Sample Recall proportion (B) = 0.30, i.e. 30% of the sample of 200 recalled commercial B. ll proportion --A ll proportion --B )/(150+200) use "pooled" p-bar Issue: Men and women stopping and asking question. BusQues: Are women more likely to stop and ask questions than men? Data: Automobile Association of America survey (January 2006) -- sample of 811 women and 750 men: "If you and your spouse are driving together and become lost, would you stop and ask for directions?" Sample results: Yes Total p-bar's Women Since Ho will include '=', Men Pooled p-bar = Analysis: Normal Test for Two Proportions 1. Hyp's 2. TeStat: 1) 2) 3. SigLev: alpha = 0.05 4. Rej Rule: 5. Calculations: 6. Concl: Answer: en and 750 men: nd ask for directions?" l include '=', 1--Yes, 0--No Women Men 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 Issue: Men and women stopping and asking question. BusQues: Are women more likely to stop and ask questions than men? Data: Automobile Association of America survey (January 2006) -- sample of 811 women and 750 men: "If you and your spouse are driving together and become lost, would you stop and ask for directions?" Sample results: Yes Total p-bar's Women 309 811 0.381 Since Ho will include '=', Men 254 750 0.339 Pooled p-bar = Analysis: Normal Test for Two Proportions 1. Hyp's Ho: pW <= pM Ha: pW > pM 2. TeStat: 1) pbarW-pbarM, difference in two sample means 2) if Ho is true (pw=pM), this is Normal with mean = 0 and StdErr = 3. SigLev: alpha = 0.05 4. Rej Rule: Reject Ho if pbarW-pbarM > 5. Calculations: pbarW-pbarM = 0.042 p-value = 0.041 0.040 6. Concl: Do not reject Ho Answer: Based on these samples (811 women and 750 men), there is strong evidence to conclude that women are more likely to stop and ask for directions than men. For these samples, about 38% of women but only 34% of mean indicated that they would stop and ask for directionsif lost en and 750 men: nd ask for directions?" l include '=', 0.361 0.024 1--Yes, 0--No Women Men 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 QUIZ 2-1 PREPARATION 1) Reread the Module 2 Objectives -- in the Learning Guide. 3) Review the HW Solution Guides. 2) Review the Module 2 Class Notes and Practice Exercises. 4) Work/Setup extra problems from the textboo OVERVIEW: Module 1 (review) and Module 2 Statistical Hypothesis Tests STATISTICAL INFERENCE INVOLVING HYPOTHESES / CLAIMS FOR BUSINESS ISSUE A certain group (population) and a key property (variable) -- perhaps several groups to compare BUS QUES Does some parameter (mu, p, var, distribution) differ from a given value? (1-sided or 2-sided) Do some parameters (mu's, p's, var's, distributions) differ from each other? (1-sided or 2-sided) DATA Identify the sample (s) from the group (s) with values of the property (variable). Sample size n (s). State any assumptions/conditions you believe to be true. ANALYSIS The Appropriate Statistical Hypothesis Test 1 Hypotheses: Ho: Will always include an equality that will be tested. Ha: The business question a 2. Test Stat: (1) Name/define what will be calculated (and examined) from the sample, and (2) If Ho is true, identify the sampling distribution of this test statistic. 3. Sig Level: alpha, the small risk of rejecting Ho when it is true that we will accept. 4. Reject Rule: "Reject Ho if …" -- test statistic values that very rarely (alpha) occur -- when Ho is 5. Calculations: From the sample results, calculate (1) Value of the Test Statistic and (2) the p-valu likelihood of these sample results (or results further from Ho) if Ho were true. 6 Conclusion "Reject Ho" or "Do Not Reject Ho." BUS ANS Best answer to the business question -- including proper qualifications. Mod 1. Claims/Hypotheses One Population Test Statistic (If Ho true:) (sigma known) Normal Test for Mean x-bar -- sample mean (sigma unk, pop ~Norm or n large) t Test for Mean t = (x-bar - muo) / s/n^.5 mu mu TEST: proportion, p (n large) variance (pop ~Normal) distribution across k categories (p1, p2, …,pk) Normal Test for Prop'n ChiSq Test for variance ChiSq Goodness of Fit Test (Normal distribution) (t distribution) p-bar, sample proportion (Normal distribution) ChiSq = (n-1)*s^2/varo (ChiSq distribution) ChiSq =Sum (e-f)^2/e (ChiSq distribution) These are the three new hypothesis tests of Module 2: Mod 2. Comparisons Involving More Than One Population two mu's TEST: (indep samples, pop's ~Norm) 2 Sample t-Test (paired samples~D's, D's ~Normal) Paired t-Test two mu's two p's (indep samples, n's large) Normal Test for 2 Prop'ns Test Statistic (If Ho true:) t = (xbar1-xbar2) /(s1^2/n1+s2^2/n2)^.5 (t distribution) t = x-bar(D)/(s(D)/(n)^.5) (t distribution) p-bar1 - p-bar2 (Normal distribution) Excel Functions --> for Reject Values: NORMINV: enter probability below value desired TINV: enter 2-tail prob associated with value desired CHIINV: enter probability above value desired Excel Functions --> for p-Values NORMDIST: returns probability below value en TDIST: returns probability in tails (1 or 2) assoc CHIDIST: returns probability above value enter tion Guides. blems from the textbook. ral groups to compare (1-sided or 2-sided) r? (1-sided or 2-sided) ble). Sample size n (s). The business question as a math statement om the sample, and will accept. pha) occur -- when Ho is true. Note 1-sided or 2-sided. tatistic and (2) the p-value, the o) if Ho were true. Reject Value(s) p-Value NORMINV NORMDIST TINV TDIST NORMINV NORMDIST notes mean = mu StdErr = sigma/n^.5 df = n-1 mean = p StdErr = (p*(1-p)/n)^.5 CHIINV CHIDIST df = n-1 CHIINV CHIDIST All e's >= 5 df = k-1 Reject Value(s) p-Value notes TINV TDIST Excel Tool: t-test: 2 sample assuming unequal variances (df = formula) TINV TDIST Excel Tool: t-test: paired 2 sample for means (df=n-1) mean = p1 - p2 Std NORMINV NORMDIST Err1 = [p1*(1-p1)/n1 + p2*(1p2)/n2]^.5 1 If Ho: p1=p2, use pooled est of p (pbar) in formula. Std Err = (pbar*(1pbar)*(1/n1+1/n2))^.5 bability below value entered. ity in tails (1 or 2) associated with value entered. bility above value entered. ...
View Full Document

Ask a homework question - tutors are online