A U.S. Department of Transportation study (July, 2001) of the level of cell phon
ID: 3158266 • Letter: A
Question
A U.S. Department of Transportation study (July, 2001) of the level of cell phone use by drivers while they
are in the act of driving a motor passenger vehicle found that for a random sample of 1,165 drivers selected
across the country, 35 were using their cell phone.
1) Form a 95% confidence interval for the proportion of drivers who use their cell phone while they are in the
act of driving their vehicle.
2) Conduct a test at =.05 to determine if the true driver cell phone use rate differs from .02.
Explanation / Answer
1.
Note that
p^ = point estimate of the population proportion = x / n = 0.030042918
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.005001317
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.959963985
Thus,
Margin of error = z(alpha/2)*sp = 0.009802401
lower bound = p^ - z(alpha/2) * sp = 0.020240518
upper bound = p^ + z(alpha/2) * sp = 0.039845319
Thus, the confidence interval is
( 0.020240518 , 0.039845319 ) [ANSWER]
****************************
2.
Formulating the null and alternatuve hypotheses,
Ho: p = 0.02
Ha: p =/= 0.02
As we see, the hypothesized po = 0.02
Getting the point estimate of p, p^,
p^ = x / n = 0.030042918
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.004101711
Getting the z statistic,
z = (p^ - po)/sp = 2.44847043
As this is a 2 tailed test, then, getting the p value,
p = 0.014346421
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the true driver cell phone use rate differs from 0.02 at 0.05 level. [CONCLUSION]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.