Statistics - Hypothesis Testing

(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?

(11.24) In a bumper test, three types of autos were deliberately crashed into a barrier at 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 crash damages the same for these three vehicles? State the decision rule for α = .05 and make the decision. Interpret the p-value.

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

(10.44) Does lovastatin reduce the risk of heart attacks? In a Texas study, researchers gave lovastatin to 2,325 people and inactive substitute to 2,081 people. After 5 years 57 of the lovastatin group had sufford a heart attack, compared with the 97 for the inactive pill.
A) State the appropriate hypothesis
B) Obtain statistic and p-value. Interpret the results at a=.01
C) Is normality assured?
D) Is the difference large enough to be important
E) What else would medical researchers need to know before prescribing this drug widely?

(10.46) To test the hypothesis that students who finished an exam first get better grades. Professor Hardtack kept the mean score of 77.1 with a standard deviation of 19.6 while the last 24 papers handed in 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.
C) Is the difference in the mean scores large enough to be important?
D) Is it 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 Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $2.14. The mean appears to be very close but not the variances. At a=.05 is there a difference in variances?