Chapter 9.2, Problem 9.39E

a)

To determine

To perform hypothesis test for one sample proportion $\widehat{p}$ .

Answer to Problem 9.39E

There is enough evidence to support the claim that fewer than half of all drivers use cell phone while their vehicles are movingat 0.05 significance level.

Explanation of Solution

Given:

Sample size = n = 70

  $x$ = 21

Formula:

Sample proportion:

  $\widehat{p}=\frac{x}{n}$

Test statistic:

  $z=\frac{\widehat{p}-p_0}{\sqrt{p_0(1-p_0)/n}}$

Calculation:

The sample proportion is,

  $\widehat{p}=\frac{21}{70}=0.3$

Null and alternative hypothesis:

  $\begin{array}{l}{H}_o:p=0.5\\ H_a:p<0.5\end{array}$

This corresponding to a left-tailed test, for which a z-test for one population proportion needs to be used.

Test statistic:

  $z=\frac{0.3-0.5}{\sqrt{0.5(1-0.5)/70}}=-3.35$

Test statistic z = -3.35

Using the P-value approach:

P(Z<-3.35) = 0.0004

Using excel formula, =NORMSDIST(-3.35)

The p-value is p = 0.0004

And a = 0.05

Since p = 0.0004 <0.05, it is concluded that the Null Hypothesis is rejected.

Conclusion: There is enough evidence to support the claim that fewer than half of all drivers use cell phone while their vehicles are moving.

b)

To determine

To explain whether there is bias in the study.

Answer to Problem 9.39E

Yes, the study is biased.

Explanation of Solution

The cameras were placed with the subject knowledge and thus it is likely that the subject will adjust their behavior as they are aware of the cameras. This will create a bias. This bias is called response bias.