*Applied Statistics*

http://www.stat.ucla.edu/~dinov/ |

- (
**HW_6_1**) A study was conducted to compare the effectiveness of two brands of**fly spray**as fly repellents. 18 boards were coated in honey. The ends of 9 were sprayed with brand**A**and the other 9 sprayed with brand**B**. 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 your**hypotheses**,**show your work**to get the statistics and**interpret the results**.

- Treating the data as from two independent samples (with the
brand
**A**data as sample 1 and the brand**B**data 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.

- (
**HW_6_2)**An advertisement for, a drug prescribed for seasonal allergic hay fever, reported the results of a double blinded study in which 374 patients took*Seldane-D*and 193 took a*Seldane-D**placebo*, (*Time*, March 27, 1995, p. 18). Headaches were reported as a side effect by 65 taking the drug and by 43 taking the placebo. Address in a statistical manner the hypothesis that the between group__difference in the proportions__of patients reporting headaches are significant.

- (
**HW_6_3)**A quality control officer of a large metal pin manufacturer wants to assess the breaking strength of more cost efficient alloy pins and see if the new alloy material will meet the spec requirements for the pins. A random sample of 5 alloy pins is taken and their breaking strengths obtained in*psi*units, {42,110; 42,550; 41,895; 42,285, 41,990}. What is your recommendation on whether we should adopt the new (cost effective) alloy manufacturing process, assuming the required breaking strength of the pins should be 42,300*psi*.