STAT E100 Section Week 10 – Hypothesis testing, 1- Proportion, 2- Proportion – Z tests, 2- Sample T tests

Course Review - Changing the recorded section time this coming week, more details to come. - Slides are posted on the website under > sections > Kela’s section - Project guidelines, get started early! - It’s worth 15% of the overall grade. The more time you have, the more feedback that you can get. - The exams are graded, see your TA for your midterm exam. - If you did not do as well as you hoped, remember, the midterm is worth 20% (undergraduates) or 15% (graduate students). - Exams are cumulative, about 20% future exams will be old stuff. - your TA to join the study group!

Key Inference Concepts and Equations: Two main inferential techniques: Confidence Intervals - for estimating values of population parameters Hypothesis Testing- for deciding whether the population supports a specific idea/model/hypothesis The results of the tests should agree!

A test of the null hypothesis H0: μ = μ 0 gives a test statistic z = –1.85. a) What is the p-value if the alternative is HA: μ > μ 0 ? b) What is the p-value if the alternative is HA: μ < μ 0 ? c) What is the p-value if the alternative is HA: μ ≠ μ 0 ? d) Would the 95% confidence interval for the true mean μ contain the value μ 0 ? Why? e) Would the 90% confidence interval for the true mean μ contain the value μ 0 ? Why? Homework Review

A large study conducted in 2000 showed that adult men spent an average of 11 hours a week watching sports on television. A random sample of 16 adult men this year showed that they now spend an average of 9 hours a week watching sports on television. The standard deviation of these 16 values was 3 hours. c) Show how the test of hypothesis results in part (a) are consistent with the confidence interval results in part (b). Homework Review

Key Equations: For 1-proportion z- significance: For 1-proportion z- interval: For interval and hypothesis test to be valid, we need both: np ≥ 10 and n(1 – p) ≥ 10

Key Equations: For 2-proportion z- significance: with pooling: For 2-proportion Z - interval:

Key Equations: For 2 sample t- significance: For 2 sample t- interval: In the formula, t* is the value from the t df distribution, with degrees of freedom df = min(n 1 -1, n 2 -1), with area between –t* and t*.

53% of Harvard Extension School students are female. 121 of the 205 students in Stat E100 are women. Is there evidence that there is a bias in the students who enroll in Stat E100? Sample Question #1

53% of Harvard Extension School students are female. 121 of the 205 students in Stat E100 are women. Is there evidence that there is a bias in the students who enroll in Stat E100? 1-proportion z- significance test Ho: p 0 = p hat = 0.53 Ha: p 0 ≠ p hat = 0.53 Since p > 0.05, we cannot reject the null hypothesis that the proportion of female Harvard Extension School students is the same as the proportion of female Extension School students that enroll in Stat E100. There is not enough evidence to suggest that there is a bias in the students that enroll in Stat E100. Sample Question #1

In David Ortiz of the Boston Red Sox was lauded for being a “clutch hitter.” That is, he batted much better with runners in “scoring position” than in all other situations. The data is as follows: situation outcome | clutch other | Total hits | | 625 outs | | Total | | 2157 a) What proportion of the time did Ortiz get a hit during clutch situations ( )? What about during the other situations? Perform a 2-sample proportion test to determine whether David Ortiz truly is a different hitter in clutch situations. Sample Question #2

In David Ortiz of the Boston Red Sox was lauded for being a “clutch hitter.” That is, he batted much better with runners in “scoring position” than in all other situations. a) What proportion of the time did Ortiz get a hit during clutch situations ( )? What about during the other situations? Perform a 2-sample proportion test to determine whether David Ortiz truly is a different hitter in clutch situations. 2-proportion z- significance test H o : p 1 - p 2 = 0 H a : p 1 - p 2 ≠ 0 Since p < 0.05, we can reject the null hypothesis that David Ortiz truly is not a different hitter in clutch situations. We have evidence to suggest that David Ortiz truly is a “clutch hitter”. Sample Question #2

Is sex related to family size? In a survey of the stat 104 students last year, students were asked to report their sex and family size (how many children in your family?). Of the 70 female students, the mean number of children was with sd = Of the 41 male students, the mean number of children was with sd = Is there statistical evidence to support the claim that family size of Harvard students is related to sex? Sample Question #3

Is sex related to family size? In a survey of the stat 104 students last year, students were asked to report their sex and family size (how many children in your family?). Of the 70 female students, the mean number of children was with sd = Of the 41 male students, the mean number of children was with sd = Is there statistical evidence to support the claim that family size of Harvard students is related to sex? 2- sided t- significance test H o : μ f - μ m = 0 H a : μ f - μ m ≠ 0 Since p > 0.05, we cannot reject the null hypothesis that there is no relationship between family size and sex. We do not have evidence to support the claim that family size of Harvard students is related to sex. Sample Question #3