10.30 In Dallas some fire trucks were painted yellow instead of red to heighten their visibility. During a test period, a fleet of fire red trucks 153,348 runs and had 20 accidents. While the fleet of yellow trucks made 135,035 runs and had 4 accidents At a (P [Rejecting the null hypothesis |Null hypothesis is true]). =.01 did the yellow fire trucks had a significantly lower accident rate? (a) State the hypothesis. (b) State decision rule and sketch it. (c) Find the sample proportions and z test statistics. (d) Make a decision. (e) Find the p- 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 (P [Rejecting the null hypothesis |Null hypothesis is true]).
10.44 Does lovestain (a cholesterol lowering drug) reduce the risk of heart attack? In a Texas study researchers gave lovestain to 2,325 and an inactive substitute to 2,081 people (average age 58). After 5 Years, 57 of the lovestain group had suffered a heart attack compared with 97 for the inactive pill. (a) state appropriate hypothesis (b) obtain a test statistic and p-value. Interpret the results At a (P [Rejecting the null hypothesis |Null hypothesis is true]) =.01. (c) Is normality assured (d) Is the difference large enough to be important? (e) What is else do medical researchers need to know before prescribing this drug widely?
10.46 To test hypothesis that students who finish an exam finish first get better grades, Professor hardback keep track of the order in which paper where handed in. The first 25 papers showed a mean score of 77.1 and a standard deviation of 19.6. While the last 24 papers showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference At a= .05? (a) state the hypothesis for a right tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is reasonable to assume equal variances? (e) Carry out a formal test for equal variances at a = .05 showing all steps clearly.
10.56 A sample of 25 concession stand purchases at the October 22 matinee of Bridge and Chucky showed a mean of purchase of $5.29 with a standard deviation of $ 3.02 .For the October 26 evening showing for the same movie, for a sample of 25 purchases the mean was $ 5.12 with a standard deviation of $ 2.14. The means appear to be really close but not the Variances At a=.05 is there a difference in variances? Show all steps clearly including an illustration of the decision rule.
11.24 In a bumper test, three types of autos were deliberately crashed into a barrier of 5 mph and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean car crashes the same of these three vehicles?
Goliath Varmint Weasel
1,660 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
For the five statistics problems in this posting, the solutions fully answer all the questions and show all the calculations including graphs where appropriate.