*Introduction to Statistical Reasoning*

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HW_7_1) An advertisement for, a drug prescribed for seasonal allergic hay fever, reported the results of a double blinded study in which 374 patients tookSeldane-Dand 193 took aSeldane-Dplacebo, (Time, March 27, 1995, p. 18). Headaches were reported as a side effect by 65 taking the drug and by 43 taking the placebo. Calculate a 95% confidence interval for thedifference in the proportionsof patients reporting headaches between the group receivingand the group receiving theSeldane-Dplacebo.

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HW_7_2) A study was conducted to compare the effectiveness of two brands offly sprayas fly repellents. 18 boards were coated in honey. The ends of 9 were sprayed with brandAand the other 9 sprayed with brandB. One of each type of board was used under each of nine different environmental conditions. (It is known that the fly populations differ, depending on environment.) For each board, the number of flies that landed on it during a 30 minute period was recorded. The resulting data is as follows:

Environment: 1 2 3 4 5 6 7 8 9 Mean Standard Deviation Brand A:23 17 28 48 10 36 15 22 94 32.56 ___ Brand B:36 22 25 60 16 34 28 22 104 38.56 ___ Difference: _ _ _ _ _ _ _ _ _ ___ -->

- Complete the table.
- In this question you will perform 2 different types of analyses on the above data.
Both of these tests may not be appropriate; you will discuss this issue in part (c). For the two tests please clearly state yourhypotheses,show your workto get the statistics andinterpret the results.

- Treating the data as from two independent samples (with the brand
Adata as sample 1 and the brandBdata as sample 2), carry out a 2-sided t-test to investigate whether there is a difference between the two brands in the average numbers of flies landing on the boards.- Treating the data as paired, carry out a 2-sided t-test to investigate whether there is a difference between the two brands in the average numbers of flies landing on the boards.
- Should we treat the data as from two independents samples or from paired data? Briefly justify your answer. Draw an appropriate dotplot for this dataset. Which of the tests from part (b) is most appropriate for this data? Justify your answer.

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/