WARM – UP ( just do “a.” ) The Gallup Poll asked a random sample of 1785 adults, “Did you attend church or synagogue in the last 7 days?” Of the respondents, 750 said “Yes.” a.)Find the 99% Confidence Interval for the % of all adults who attended church or synagogue during the past week. (Follow all steps) b.)Do the results provide good evidence that less than half of the population attend church or synagogue? Give supporting evidence? (Follow all steps)

We can be 99% confident that the true proportion of adults who attended church or synagogue in the past 7 days is between 39.0% and 45.0%. 1.SRS – Stated 2. Appr. Normal: 1785(0.420) ≥ (1 – 0.420) ≥ 10 3.Population of Adults ≥ 10(1785) One Proportion Z– Conf. Int. a.)Find the 99% Confidence Interval for the % of all adults who attended church or synagogue during the past week. (Follow all steps) The Gallup Poll asked a random sample of 1785 adults, “Did you attend church or synagogue in the last 7 days?” Of the respondents, 750 said “Yes.”

P-value ≤ Reject H 0 -Evidence supporting H a P-value > Fail to Reject H 0 - No Evidence supporting H a Decision Conclusion Decision Conclusion Chapter 21 – More about Tests

b.)Of 1785, 750 said “Yes.” Do the results provide good evidence that less than half of the population attend church or synagogue? Give supporting evidence? (Follow all steps) Since the P-Value is less than α = 0.05 we REJECT H 0. There is sufficient evidence that The % of adults attending church or synagogue is less than 50%. p = The true proportion of adults that attend church or synagogue in the past 7 days. H 0 : p = 0.50 H a : p < 0.50 One Proportion z – Test 1.SRS: Stated 2. Appr. Normal: 1785(0.50) ≥ (1 – 0.50) ≥ 10 3.Population of Adults ≥ 10(1785)

p = The true proportion of Hispanics called for jury duty in the county. H 0 : p = 0.19 H A : p < 0.19

p=The true proportion of Hispanics called for jury in the county. H 0 : p = 0.19 H A : p < 0.19 One Proportion z – Test SRS: potential jurors are called randomly from all of the residents. 10% condition: Population of jurors in the county > 10(72) Success/Failure condition: np= (72)(0.19) = and n(1 – p) = (72)(0.81) = are both > 10, so the sample is large enough. The conditions have been satisfied, so a Normal model can be used to model the sampling distribution of the proportion, Since the P-value = is somewhat high p>0.05, we fail to reject the null hypothesis. There is NO convincing evidence that Hispanics are underrepresented in the jury selection system.

What can you say if the P-value does not fall below  ? –You should say that “The data have failed to provide sufficient evidence to reject the null hypothesis.” –NEVER “accept the null hypothesis”. ONLY “Fail to Reject the null hypothesis.”

Chapter 21 – More about Tests Common alpha levels are 0.10, 0.05, and – When we reject the null hypothesis, we say that the test is “significant at that level.” significance level.The alpha level, α =0.05,is also called the significance level.

Homework- Page 491: 1,2,5a,6a, 8-10

H 0 : p = 0.40 (p=The proportion of female executives.) H A : p < 0.40

H 0 : p = 0.40 (The proportion of female executives.) H A : p < 0.40 One Proportion z – Test Randomization condition: Executives were not chosen randomly, 10% condition: Population of employees at the company > 10(43) np= (43)(0.40) = 17.2 n(1 – p) = (43)(0.60) = 25.8 Success/Failure condition: np= (43)(0.40) = 17.2 and n(1 – p) = (43)(0.60) = 25.8 are both >10, so the sample is large enough. so we continue with Caution The conditions have not all been satisfied, so a Normal model may or may not be valid, so we continue with Caution.

fail to reject the H 0 Since the P-value = is high (p>0.05), we fail to reject the H 0. There is little evidence to suggest proportion of female executives is any different from the overall proportion of 40% female employees at the company.

When the alternative is two-sided, the critical value splits  equally into two tails: Confidence Intervals and Hypothesis Tests A confidence interval with a confidence level of C% corresponds to a two-sided hypothesis test (The “≠” test) with an  -level of 100 – C%. If the test “REJECTS H 0 ”, then the sample statistic will NOT be in the interval

You can also reject using just the z-score. – Any z-score larger in magnitude than a particular critical value leads us to reject H 0. –Any z-score smaller in magnitude than a particular critical value leads us to fail to reject H 0.  1-sided2-sided