The following data are based on a study of the relationship between car accident

Question

The following data are based on a study of the relationship between car accidents and the use of cellular phones. Objective of the study is to show that using a cellular telephone while driving increases the chances of a car accident. a) In the table above, identify the sample that you need to use to estimate the probability of having a car accident when using a cellular telephone while driving, and compute the estimate of this probability. b) Find an 90% confidence interval for the probability of having a car accident while using the cellular telephone. c) What does the phrase 90% confident" mean? d) In the table above, identify the sample that you need to use to estimate the probability of having a car accident when not using a cellular telephone while driving, and compute the estimate of this probability. e) Find an 90% confidence interval for the probability of having a car accident when not using the cellular telephone f) Do the intervals from part b and e overlap? What do you think this means about the danger of using a cellular telephone while driving? g) Let p1 denote the probability of having a car accident while using a cellular telephone, and let p2 denote the probability of having a car accident while not using a cellular telephone. Describe the null and alternative hypothesis for the problem of showing that using a cellular telephone while driving increases the chances of a car accident. Ho: Ha: h) Do the data support the fact that using a cellular telephone while driving increases the chances of a car accident? Use a significance level alpha = 0.1. Use both methods (p-value and the critical value approach) i) Calculate an appropriate confidence interval (two sided or lower or upper bond) and explain how it can be used to test the hypotheses. Does this interval contain zero? What does that mean?

Explanation / Answer

a) estimated probability of having accidents when using cellular phone = 23/305 = 7.54%

n = p(1-p) * z^2/ d^2

z = 1.96 (at 0.05 alpha levels for 2 tail)

d = margin of error, it is not given here. Let us assume the estimate should be within 2%

n = 0.9246* 0.754*1.96*1.96/0.02^2 = 670

b) 90% CI = p +/- z*sqrt(p(1-p)/n) where z = 1.65 for 90% confidence level 2 tail

Upper CI = 5%

lower CI = 10%

c) answers are 1,4 and 5

All 3 statements say that when we take repeated samples 90% of the samples will have confidence intervals that contain the population proportion

d) Using the same method as answer a)

estimated probability of having accidents when NOT using cellular phone = 26/427 = 5.74%

n = p(1-p) * z^2/ d^2

n = 520

e) 90% CI = p +/- z*sqrt(p(1-p)/n) where z = 1.65 for 90% confidence level 2 tail

Upper CI = 3.9%

lower CI = 7.5%

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