Testing Proportion Hypothesis Claim is going to be a percent: “85% of all high school students have cell phones” “Less than 20% of seniors take the bus to school” “Most juniors take the SATs” Classic P - values (and the calculator, maybe)

Classic 1.Write the claim as a comparison of a percent E.g., “Most juniors take the SATs” becomes “p > 0.5” 2.Write the null and alternate hypothesis H 0 : p ≤ 0.5 H 1 : p > Critical value from the z table always

Classic, part 2 4.The test statistic: p is the benchmark proportion (from the hypothesis) p is the sample proportion q is 1 – p 5.Required: np > 5 and nq > 5

Testing a Hypothesis Claim: 4 out of 5 dentist recommend daily flossing –In a poll of 84 dentist, 70 recommended flossing once a day –DoC = What is your estimate of the number of south students who have seen “The King’s Speech”? –Let’s take a poll –Degree of Confidence

Proportion Worksheet Original claim Label null and alternative hypothesis Opposite claim Sample proportion =x =n = Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?

Proportion Worksheet Original claim Label null and alternative hypothesis Opposite claim Sample proportion =x =n = Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?

Testing a Hypothesis Claim: a majority of Americans support intervention in Darfur –In a poll of 250 people, 140 agreed that the we should intervene in the war –Degree of confidence:

Proportion Worksheet Original claim Label null and alternative hypothesis Opposite claim Sample proportion =x =n = Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?

Proportion Worksheet Original claim Label null and alternative hypothesis Opposite claim Sample proportion =x =n = Degree of confidence Test statistics Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?

Using the calculator STAT TESTS 5: 1-PropZTest –p 0 : The benchmark –x: # of ‘successes’ –n: # of samples –prop  p 0 p 0 Alternate hypothesis

Homework 1.Test the claim that less than one quarter of the population has passports. In a poll of 36 people, 10 had passports. Use a degree of confidence of 90% 2.The CEO claims that 80% of her customers are satisfied with their service. The local newspaper sampled 100 customers; 73 say they are satisfied. Use a 99% degree of confidence to test the claim sampled trees were tested for traces of infestation; 153 of the trees showed such traces. Test the claim that more than 10% of the trees have been infested. (Use a 5% level of significance)

More homework 4.Suppose that you interview 600 voters about who they voted for governor. 330 reported that they voted for the democratic candidate. Can we claim that the democratic candidate will win the election at the.01 significance level? 5.In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 1% significance level, test the claim that the failure rate is now lower if a sample of 1520 current job applicants results in 58 failures.

Homework #1 Original claimp < 0.25 (H1) Label null and alternative hypothesis Opposite claimp ≥ 0.25 (H0) Sample proportion =x = 10n = 36 Degree of confidence90% Test statisticsp = 0.278, z = Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?FRT null, FTR original claim p-value = 0.65 > 0.1Ditto

Homework #2 Original claimP = 0.8 (H 0 ) Label null and alternative hypothesis Opposite claimp ≠ 0.8 (H 1 ) Sample proportion =x = 10n = 36 Degree of confidence90% Test statisticsp = 0.73, z = Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?FRT null, FTR original claim p-value = 0.08 > 0.01Ditto

Homework #3 Original claimp > 0.1 (H1) Label null and alternative hypothesis Opposite claimp ≤ 0.1 (H0) Sample proportion =x = 153n = 1500 Degree of confidence95% Test statisticsp = 0.102, z = Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) 1.64 Critical value (from Z table) Reject or accept?FRT null, FTR original claim p-value = > 0.05Ditto

Homework #4 Original claimp < (H1) Label null and alternative hypothesis Opposite claimp ≥ (H2) Sample proportion =x = 330n = 600 Degree of confidence99% Test statisticsp = 0.55, z = 2.45 Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) 2.33 Critical value (from Z table) Reject or accept?Reject null, Accept original claim p-value = < 0.01Ditto

Homework #5 Original claimp < 0.25 Label null and alternative hypothesis Opposite claimp ≥ 0.25 Sample proportion =x = 58n = 1520 Degree of confidence99% Test statisticsp = 0.038, z = Critical region Two-tailed (H 0 =) Left tailed (H 0  ) Right tailed (H 0  ) Critical value (from Z table) Reject or accept?Reject null, Accept original claim p-value = 0 < 0.01Ditto