RES/342 Week 4 Answer Guide - Statistics
This Week's Text Assignment is:
Chapter 10 – Chapter Exercises 10.30, 10.44, and 10.52
Chapter 11 – Chapter Exercise 11.24
Chapter 15 – Chapter Exercises 15.18 and 15.28
Problem 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.
a)
H0: p1 = p2
H1: p1 > p2
b)
We will reject Reject H0 if z > 2.326
c)
p = 24 / (153348 + 135035) = 0.00008322
(20 / 153348) - (4 / 135035) / √0.00008322(1 - 0.00008322) = 2.96
p1 – p2 = 0.000100762
d)
The null hypothesis is rejected because our test statistic is within the region of rejection, with z > 2.36.
e)
pvalue = 0.0015. This will cause us to reject the null hypothesis.
f) Yes, the difference is large enough to make a difference. The change could save lives and money for the fire department. It would also be beneficial to city inhabitants.
g) Yes, normality is fulfilled because there is a large enough sample data set.
Problem 10.44
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret the results at α = .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? (Data are from Science News 153 [May 30, 1998], p. 343.)
a)
H0: p1 = p2
H1: p1 < p2
b)
p = 154 / (2325 + 2081) = 0.034952
√ [ (0.035) (0.965) (1 / 2325 + 1 / 2081) ] =
√ [ (0.035) (0.965) (0.0009 ] = 0.005546
(57 / 2325 – 97 / 2081) / 0.005546 = -3.98
These results will cause us to reject the Null Hypothesis because the α = .01. Our null hypothesis is p1 = p2 and is not supported by these results.
c)
Yes, normality can be assumed due to the large sample size.
d)
Yes, the difference is large enough and this even small changes are significant in drug testing.
e)
Medical researchers should do additional tests to see if they are consistent with these results. A slight change in the test parameters could result is much different results.
Problem 10.52
One group of accounting students took a distance learning class, while another group took the same course in a traditional classroom. At α = .10, is there a significant difference in the mean scores listed below? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the test statistic. (d) Make a decision. (e) Use Excel to find the p-value and interpret it.
a)
H0: p1 => .10
H1: p1 < .10
b)
We will reject H0 if the z < 0.10.
Problem 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?
Groups |
Count |
Sum |
Average |
Variance |
Goliath |
5 |
6410 |
1282 |
246320 |
Varmint |
5 |
6880 |
1376 |
103580 |
Weasel |
5 |
8190 |
1638 |
195170 |
After running ANOVA test in MegaStat I got the following results:
F = 0.9367
P-Value = 0.4188
The Null Hypothesis will not be rejected because p > 0.05.
Problem 15.18
Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned?
H0: At α = .01 degree of uncertainty is independent.
H1: At α = .01 degree of uncertainty is not independent.
Chi Square statistic
Problem 15.28
Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.)
Chi Square = 0.63…
P-Value = 0.43
I prefer the Chi Square test because it requires a greater amount of effort, which gives me sense of satisfaction. I also feel more confident with the results of a chi square test.
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