9.5 Notes Testing Differences of Two Means/Proportions (Independent Samples)

Independent – Ex. Separate a class into two groups and teach each group with a different technique. Then test each group. Non-ex. Test a group of students before learning. Then test them after to see how much they learned. 3 Types of questions:

I.Difference of means where both σ 1 and σ 2 are known Process is the same as μ where n > 30 except:

Ex. 1 A teacher wishes to compare the effectiveness of two teaching methods. Students are randomly divided into two groups. The first group is taught by method 1; the second group, by method 2. At the end of the course, a comprehensive exam is given to all students. The teacher claims that the second method will increase the mean score on the comprehensive exam. The first group consists of 49 students with a mean score of 74.8 and σ = 14 points. The second group has 50 students with a mean score of 81.3 and σ = 15 points. Is the teacher’s claim justified at the 5% level of significance?

I.Difference of means where either σ 1 and σ 2 are unknown Process is the same as μ where both σ 1 and σ 2 are known except:

Ex. 2 Two competing headache remedies claim to give fast-acting relief. An experiment was performed to compare the mean lengths of time required for bodily absorption of brand A and brand B headache remedies. Assume the absorption rate for each remedy is approximately normal. Twelve people were randomly selected and given an oral dosage of brand A. Another 12 were randomly selected and given an equal dosage of brand B. The length of time in minutes for the drugs to reach a specified level in the blood was recorded. The means and standard deviations for the two samples follow: Brand A: = 20.1 min.s 1 = 8.7 min. Brand B: = 18.9 min. s 2 = 7.5 min. Test the claim that there is no difference in the mean time absorption rates for these two medicines at the 5% level of significance.

Assignment P. 470 #3, 7, 8, 9, 11, 13, 17

III.Difference of proportions Process is the same as difference of means where both σ 1 and σ 2 are known except:

Ex. 3 The Macek County Clerk wishes to improve voter registration. One method under consideration is to send reminders in the mail to see if that will increase voter registration. As a pilot study a random sample of 1250 people were randomly divided into 2 groups. Group 1: there were 625 people in this group. No reminders to register were sent to them. The number of potential voters from this group who registered was 295. Group 2: This group also contained 625 people. Reminders were sent in the mail to each member in the group, and the number who registered to vote was 350. Use a 5% level of significance to test the claim that mail reminders improve voter registration.

Assignment P. 471 #10, 12, 14, 18, 25, 27, 29