Problem 4: In a 2001 study concerning the effect of cell phone use on driving ab
ID: 3061676 • Letter: P
Question
Problem 4: In a 2001 study concerning the effect of cell phone use on driving ability, 32 subjects used a machine that simulated driving situations and were asked to press a brake button when they saw a red light. Each of the 32 subjects had their reaction time measure twice: once when they were talking on a cell phone and once when they were out. For each subject, the difference between the reaction time when using a cell phone and the reaction time when not using a cell phone was recorded. These 32 differences had a mean of 50.6 milliseconds and a standard deviation of 52.5 milliseconds. Can you conclude that on average, cell phone use slows down reaction time?Explanation / Answer
Solution:-
n = 32
dbar = 50.6, S.D = 52.5
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: d< 0
Alternative hypothesis: d > 0
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).
s = sqrt [ ((di - d)2 / (n - 1) ]
s = 52.5
SE = s / sqrt(n)
S.E = 9.28078
DF = n - 1 = 32 -1
D.F = 31
t = [ (x1 - x2) - D ] / SE
t = 5.45
where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.
Since we have a one-tailed test, the P-value is the probability that a t statistic having 31 degrees of freedom greater than 5.45.
Thus, the P-value = less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
Reject H0. On average, cell phone use slows down reaction time.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.