211-01-2+Class+Notes+1-3

211-01-2+Class+Notes+1-3 - DSC 211 CLASS NOTES 1-3 Page 1...

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DSC 211 CLASS NOTES 1-3, Page 1 EXCEL functions So Far--Claims about Test Statistic: If Ho true: Reject value p-value x-bar NORMDIST -->prob below (test stat,-- , --) =TINV(2-tail prob,df) TDIST --> prob in tail(s) -t distribution, df=n-1 (t stat,df,1 or 2) NOTE: If p-value Generally Accepted "Answers" to hypothesis testing business questions If alpha = 0.10 If alpha = 0.05 If alpha = 0.01 0.05 - 0.10 "sufficient but weak evidence to conclude . .." "Insufficient evidence to conclude . ." "Insufficient evidence to conclude . ." 0.01 - 0.05 "strong evidence to conclude …" "strong evidence to conclude …" "strong but not strong enough evidence to…" < 0.01 "very strong or overwhelming evidence to…" "very strong or overwhelming evidence to…" "very strong or overwhelming evidence to…" Sample of 100 Voters New Type of Claims: Do you plan to vote for Obama? 0=no, 1=yes Let's illustrate with an example. 0 Issue: Voter Support for Obama in Montgomery County - October 2008. 1 Question: Does poll (sample n=100) support the claim that the proportion of all voters (p) who will vote for Obama is > .50? 1 Data: Polling results from random sample of 100 voters, "Do you plan to vote for Obama?" See column M. 1 1 Hypotheses: Ho: p <= .50 1 Ha: p > .50 1 2 Test Statistic: [p-bar = #who say "yes"/total sample size] 0 1 E(p-bar) = 0.50 1 [p * (1-p) / n] ^.5 = 0.050 1 Could graph this sampling distribution of p-bar: n = 100 0 p-bar f(p-bar) CumProb 0 0.34 0.05 0.00 1 0.36 0.16 0.00 1 0.38 0.45 0.01 0 0.4 1.08 0.02 1 0.42 2.22 0.05 1 0.44 3.88 0.12 0 0.46 5.79 0.21 1 0.48 7.37 0.34 0 0.5 7.98 0.50 1 0.52 7.37 0.66 1 0.54 5.79 0.79 0 0.56 3.88 0.88 1 0.58 2.22 0.95 0 0.6 1.08 0.98 1 0.62 0.45 0.99 0 0.64 0.16 1.00 1 0.66 0.05 1.00 NOTE: Could choose z as the test statistic. z = (p-bar-0.5)/(.5*.5/100)^.5 as 1 3 Sign Level: alpha = .05 textbook does. We'll use this approach (p-bar is Normal) -- more direct. 1 4 Reject Rule: Reject Ho if p-bar > the p-bar with a probability below = .95 0 Use NORMINV (.95,.50,.05) = 0.582 1 Reject Ho if p-hat > .582 0 5 Calculations Examine the sample results in Column M. 1 # of 1's = 57 =COUNTIF(M4.M103,1) 1 p-bar = 0.570 =57/100 sample proportion " I will vote for Obama." 1 p-value= 0.081 =1-NORMDIST(.57,.5,.05,TRUE) 0 6 Conclusions Do not reject Ho. 1 Answer: Evidence from the sample of only 100 (even with a sample proportion of .57) is not strong enough to conclude that 1 greater than 50% of the total Montgomery County population (ALL voters) will vote for Obama. 0 May want to do larger sampling. 1 mu (sigma known) Normal Test for Mean: -normal distrib (mu o ,sigma/n^.5) =NORMINV(prob below,-- ,-- ,true) mu (sigma not known) t-Test for Mean: t = (x-bar - mu o ) / (s/n^.5) (1) "Normal Test of a Proportion" Claims about the proportion, p , of a population that have some property or characteristic. (1)

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211-01-2+Class+Notes+1-3 - DSC 211 CLASS NOTES 1-3 Page 1...

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