Question

In a cover story, BusinessWeek published information about sleep habits of Americans file (BusinessWeek, Jan 2004). The article noted that sleep deprivation causes a number of problems, including highway deaths. Fifty one percent of adult drivers admit to driving while drowsy. A researcher hypothesized that this issue was an even bigger problem for night shift workers. A sample of 400 night shift workers identified those who admitted to driving while drowsy. See the Drowsy file for details. a. Construct a 97% confidence interval for the population percentage of adult drivers who admit to driving while drowsy. b. Use BOTH the p-value and critical value approaches to conduct a hypothesis test to determine the percent of adult drivers who admit to driving while drowsy. Use alpha=0.2

Answer 1

Solution:

a.

From the data estimate of the proportion of adult, drivers admit to driving while drowsy is:

The 97% confidence interval for the population percentage of adult drivers who admit to driving while drowsy is:

97% CI =(0.526448902, 0.633551098)

b.

We need to test the hypothesis

Ho: p=0.51

Ha: p>0.51

The value of the test statistics is given by,

p-value = P(z > 2.40) = 0.0082

critical value = Z_0.2 = 0.84

The decision rule is to reject Ho if test statistics is greater than the critical value (or if p-value <α )

Hence we reject Ho and conclude that there is sufficient evidence to support that this issue was an even bigger problem for night shift workers.