# Res 342 Week 3

Pages: 5 (1111 words) Published: March 21, 2012
Individual Assignment

RES 342

Individual Assignment: 9.12 (part a only), 9.56 (part a only), 10.4 (part a only), 10.30 (parts a through d), 10.37 (part a only), 10.38, 10.40, and

9.12 The Tri-Cities Tobacco Coalition sent three underage teenagers into various stores in Detroit and Highland Park to see if they could purchase cigarettes. Of 320 stores checked, 82 sold cigarettes to teens between 15 and 17 years old. (a) If the goal is to reduce the percent to 20 percent or less, does this sample show that the goal is not being achieved at α = .05 in a right-tailed test? (b) Construct a 95 percent confidence interval for the true percent of sellers who allow teens to purchase tobacco. (c) Explain how the confidence interval is equivalent to a two-tailed test at α = .05 (Please see attachment)

9.56 A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

10.4 A survey of 100 mayonnaise purchasers showed that 65 were loyal to one brand. For 100 bath soap purchasers, only 53 were loyal to one brand. (a) Perform a two-tailed test comparing the proportion of brand-loyal customers at α = .05. (b) Form a confidence interval for the difference of proportions, without pooling the samples. Does it include zero?

10.30 In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain. *10.30| | | | | |

H0: 1 = 2 H1: 1 > 21- Red fire trucks x = 20 n= 153,3482- Yellow fire trucks x= 4 n = 135,035significance = .01Z statisticz-critcal = 2.32Reject H0 if z cal is > than the z critical (2.32) | | | | | | | |

| p1| p2| pc| | |
| 0.000130422| 2.96219E-05| 8E-05| p (as decimal)|
| 0.000130422| 2.96219E-05| 8E-05| p (as fraction)|
| 20| 4| 24| X| |
| 153348| 135035| 288383| n| |
| | | | | |
| | 0.0001008| difference| |
| | 0| hypothesized difference|
| | 3.40428E-05| std. error| |
| | 2.960988745| z| | |
Since the z cal (2.96) is > than the z critical than the H0 is rejected.

10.37 After John F. Kennedy, Jr., was killed in an airplane crash at night, a survey was taken, asking whether a noninstrument-rated pilot should be allowed to fly at night. Of 409 New York State residents, 61 said yes. Of 70 aviation experts who were asked the same question, 40 said yes. (a) At α = .01, did a larger proportion of experts say yes compared with the general public, or is the difference within the realm of chance? (b) Find the p-value and interpret it. (b) Is normality assured?

H0: 1 ≥ 2 H1: 1 < 2
1 residents x= 61 n=409
2 experts x= 40 n=70

Significance .01

Z statistic =
z-critical 2.33

Reject H0 if z cal is < than the z critical (2.33)
| | | | | | |
| p1| p2| pc| | | |
| 0.1491| 0.5714| 0.2109| p (as decimal)| |
| 61/409| 40/70| ######| p (as fraction)| |
| 61.| 40.| 101.| X| | |
| 409| 70| 479| n| | |
| | | | | | |
| | -0.4223| difference| | |
| | 0.| hypothesized difference| |
| | 0.0528| std. error| | |
| | -8.00| z| | | |...