Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B

Today’s Agenda Overview and practice of “Big 5” inference scenarios In-Lab Project: Hypothesis testing for independent samples In-Lab Review: Hypothesis tests

Big 5 Parameters and Formulas in Yellow Card Big 5 Parameters (5 test types) p, μ, μ d, p 1 -p 2, μ 1 -μ 2 How to use the yellow card: 1.Decide the test type (and equivalently the parameter) 2.Find the corresponding table on Yellow Card page 2 3.Find then: the (test) statistics, standard errors, formula for CI, formula for computing test statistics 4.Choose the formula needed and plug in the value from the data given in the problem

Comments on Usage of Yellow Card How to decide the test type? Decide the parameter first (out of the big 5). 2 z tests and 3 t tests Always write the formula you want to use first before plugging in values. Some special cases: conservative CI and sample size for population proportion test paired-t test is grouped into mean test

And now… We have finally seen all the Big 5 inference scenarios. Do you know how to distinguish between them? Do you know when to use a confidence interval versus a hypothesis test? We will practice this now…

Research question: Do more people over 30 years of age snore than people under 30? Which method would be best for answering this question? Confidence Interval Hypothesis test

Research question: Do more people over 30 years of age snore than people under 30? What is the appropriate parameter? p p 1 – p 2 μ μ d μ 1 – μ 2

Do more older people snore? Let’s look at this in more detail… The National Sleep Foundation asked a random sample of 995 adults questions about their sleeping habits. 318 of 811 people over 30 reported that they snored at least a few nights a week; 48 of 184 people under 30 reported that they snored at least a few nights a week Compare the number of people over 30 (group 1) who snore to the number under 30 (group 2) who snore What do we know? n 1 = 811n 2 = 184 X 1 = 318X 2 = 48

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, What is the appropriate alternative hypothesis? A. H a : p 1 >p 2 B. H a : p 1 <p 2 C. H a : p 1 ≠p 2

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, Which of the following values is the only one that could be the estimate of the common population proportion? A B C. 0.43

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, We know these are independent random samples. What remaining data condition do we check? A. np ≥ 10 and n(1-p) ≥ 10 B. n 1 ≥ 10, n 1 (1- ) ≥ 10 and n 2 ≥ 10, n 2 (1- ) ≥ 10 C. n 1 ≥ 10, n 1 (1- ) ≥ 10 and n 2 ≥ 10, n 2 (1- ) ≥ 10

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, The test statistic is Z=3.33. Sketch and calculate the p-value.

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, What is your decision at a 1% level? Reject H o Fail to reject H o

Do more older people snore? n 1 = 811, n 2 = 184, X 1 = 318, X 2 = 48, Which is an appropriate real world conclusion? A. More people over 30 snore than people under 30 B. There is evidence that more people over 30 snore than people under 30. C. Both of these are appropriate conclusions. D. Neither of these is an appropriate conclusion.

Research question: On average, how much difference is there between the adult heights of a mother and her daughter? Which method would be best for answering this question? Confidence Interval Hypothesis test

Research question: On average, how much difference is there between the adult heights of a mother and her daughter? What is the appropriate parameter? p p 1 – p 2 μ μ d μ 1 – μ 2

Research question: Is there a difference between the average age at time of first marriage for men and women? Which method would be best for answering this question? Confidence Interval Hypothesis test

Research question: Is there a difference between the average age at time of first marriage for men and women? What is the appropriate parameter? p p 1 – p 2 μ μ d μ 1 – μ 2

Extra Credit Opportunity Complete the CAOS assessment between March 17 and 21 (by NOON) and you will receive 2 additional points added to your second midterm score This may be enough to move you up to the next letter grade Look for the link on Ctools > Lab Info: Second CAOS Extra Credit (March 17-21)

In Lab Project Testing means of two populations Possible questions: a. Do undergrad men and women spend the same amount of time getting ready in the morning? b. Do students who don’t live in dorms eat out more often than students who live in dorms?(meals/weak?) Complete the project in groups and each group should hand in one copy of the solution with the names of members.

Before Leaving Complete the In-Lab Review on Hypothesis Test (link from Ctools\Lab Info)