2Learning ObjectivesFormulate null and alternative hypotheses for applications involving two population means or proportionsFormulate a decision rule for testing a hypothesisKnow how to use the test statistic, critical value, and p-value approaches to test the null hypothesis
3Inference about the Difference between Two Means: Independent Samples Two random samples are drawn from the two populations of interest.Examples of independent samples;Mean difference between male and femaleMean difference between section 1 and section 2Mean difference between Thailand and Singapore
4Review: Steps in Hypothesis Testing 1. Formulate the appropriate null and alternative hypotheses 2. Specify the desired level of significance 3. Determine the rejection region 4. Obtain sample evidence and compute the test statistic 5. Reach a decision and interpret the result
5Formulate Hypotheses and Determine the Rejection Region H0 : 1 - 2 ≤ D0H1 : 1 - 2 > D0H0 : 1 - 2 ≥ D0 H1 : 1 - 2 < D0H0 : 1 - 2 = D0H1 : 1 - 2 D0D0 is a constant
8Example 2ได้มีการทดสอบฤทธิ์ยาแก้ปวดหัวสองแบรนด์ โดยวัดจากช่วงระยะเวลาในการออกฤทธิ์พบว่า ค่าเฉลี่ยและส่วนเบี่ยงเบนมาตรฐานของ Brand A และ Brand B เท่ากับ 21.8 min กับ 18.9 min และ 8.7 min และ 7.5 min ตามลำดับ โดยข้อมูลได้จากการสุ่มทดสอบยา Brand ละจำนวน 12 เม็ด สมมติให้ความแปรปรวนของระยะเวลาในการออกฤทธิ์ของประชากรทั้งสองเท่ากัน
12Example 3For the following studies, indicate whether an independent-samples or paired t test is appropriate:You want to study regional differences in consumer spending. You randomly select a sample of consumers in the Midwest and the East and track their spending patterns.You want to study differences in the spending habits of teenage boys and girls. You select 100 brother-sister pairs and study their spending behavior.
13Example 3 (Cont’)You want to compare error rates for 20 employees before and after they attend a quality improvement workshop.Weight is obtained for each subject before and after Dr. Nogani’s new treatment. The hypothesis to be tested is that the treatment has no effect on weight loss.The Jenkins Activity Survey is administered to 20 couples. The hypothesis to be tested is that husbands’ and wives’ scores do not differ.
14Example 3 (Cont’)Subjects are asked their height and then a measurement of height is obtained. The hypothesis to be tested is that self-reported and actual heights do not differ.You want to compare the durability of two types of socks. You have people wear one type of sock on one foot and another type of sock on the other. You see how long it takes for a hole to appear. (Assume they wash them periodically!)
18Exercise 1Before a training session for call centre employees a sample of 50 calls to the call centre had an average duration of 5 minutes, whereas after the training session a sample of 45 calls had an average duration of 4.5 minutes. The population variance is known to have been 1.5 minutes before the course and 2 minutes afterwards. Has the course beeneﬀective?
19Exercise 2A chain of record shops believes that its Northumberland Street store (Shop 1) is more successful than its Metro Centre branch (Shop 2). The management take a random sample of daily takings and obtains the following summary statistics:Is the management’s belief correct?
20Exercise 3An airline company, EasyAir, advertises 5 hour ﬂights from Glasgow to Cairo. Another company ﬂying the same route, RyanJet, suspects EasyAir of false advertising, and samples 20 of EasyAir’s ﬂights between Glasgow and Cairo. The mean ﬂight time from this sample is 5 hours and 10 minutes with a standard deviation of 20 minutes. Are RyanJet’s suspicions supported?
21Exercise 4The mean age of students attending a college is 19.5 years. The ages of a sample of7 students who have been oﬀered college accommodation are given below. Test the hypothesis that younger students are favoured.