Please need explanation of all steps Problem 3 The following data are based on a
ID: 3223524 • Letter: P
Question
Please need explanation of all steps
Problem 3
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.
Accident NoAccid All
NoPhone 26 427 453
Phone 23 282 305
All 49 709 758
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?
Circle correct statements - could be one or more and correct the statements you didn’t circle
1- If we repeatedly draw samples of the same size from the same population, 90 % of confidence intervals will include the true population proportion
2-There is a 0.90 probability that the true population proportion will be included in the confidence interval computed above
3-There is a 0.90 probability that the sample proportion will be included in the confidence interval computed above
4- If we sample repeatedly, about 90% of the confidence intervals will contain the true population proportion
5- If we sample 100 times , 90 of the confidence intervals will cover the true population 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 =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?
j) Sometimes the results from part f and i seem contradictory. If we want to compare whether the use of a cellular increases chances of having a car accident, which is the correct approach? Why?
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%
As per Chegg t&c I can only answer 4 parts, I have answered 5 parts.
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