Name:______________________________________ Module 4 Homework Assignment 1. Determine whether the samples are independent or dependent. The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug. Explain. Solution: Instructor Comments: 2. Determine whether the samples are independent or dependent. The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. The data consist of before and after intensities for each patient. Explain. Solution: Instructor Comments: 3. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the two age groups is the same. Use a significance level of 0.01. Show all steps of the hypothesis test and all calculations. Solution: Instructor Comments: 4. A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to construct a 99% confidence interval for 1 - 2 where 1 and 2 represent the mean for the treatment group and the control group respectively. Show all steps of the hypothesis test and all calculations. Use the following t-distribution table - http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm Treatment Group n1 = 85 189.1 Control Group n2 = 75 = 203.7 s1 = 38.7 s2 = 39.2 x1 x2 Solution: Instructor Comments: For questions 5 - 9 below, use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. Five students took a math test before and after tutoring. Their scores were as follows. Student A B C D Before 71 66 67 77 After 75 75 65 80 E 75 87 Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores. 5. State the null and alternative hypotheses. Solution: As the samples contain the same students so this is a paired data and thus the hypotheses arem Instructor Comments: H 0 : d =0H a : d 0 , and sd, 6. Find d, d Solution: Considering d = after- before the values are, D = 4, 9, -2, 3 and 12. Thus, Instructor Comments: d=5.2 and S d =5.44977 7. Find the value of the test statistic, t. Solution: Instructor Comments: Sample = T= 5.20 5.44977 5 SD Sample difference0 = 2.1336 8. Find the critical value(s) and state the decision about the null hypothesis. Solution: Instructor Comments: This is a two tailed test with 0.01 significance level. Df = sample size -1 = 4 Thus the critical values are = t ( 0.005, 4 ) = 4.6041 9. State the conclusion in non-technical terms. Solution: Do not reject the null hypothesis concluding that the data is not providing enough evidence that tutoring has an effect on the math scores at 0.01 significance level. Instructor Comments