Question

1. The advocacy group the National Safety Council (NSC) reports that cell phone use while driving leads to 1.6 million crashes each year and an astounding out of every 4 car accidents in the United States is caused by texting and driving. Hoping to show that their campaign to create awareness about the dangers of distracted driving is working and that less people are texting and driving, the advocacy group the National Safety Council (NSC) did a study of accidents that occurred in states in which they ran public service announcements and states that they did not. Using the data below, test the hypothesis, at a 95% Confidence Level, that the NSC public service announcements cause a decrease in the average number of crashes.

States with NSC Public Service Announcements                  States without NSC Public Service Announcements

n₁ = 20states                                                                                                                 n₂ =30 states

x₁ =785,000 accidents                                                                                         x₂ =815,000 accidents

σ₁ = 12,000 accidents                                                             σ₂ = 11,000 accidents

Please show all 6 steps of your work.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 < μ2

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.645.
Hence reject H0 if z < -1.645

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(144000000/20 + 121000000/30)
sp = 3351.6165

Test statistic,
z = (x1bar - x2bar)/sp
z = (785000 - 815000)/3351.6165
z = -8.95

P-value Approach
P-value = 0
As P-value >= 0.05, fail to reject null hypothesis.