Question

An insurance company would like to test the hypothesis that a difference exists in the proportion of students in12th grade who text while driving when compared to the proportion of 11th

grade drivers who text. A random sample of 160 12th grade students found that 84 texted while driving. A random sample of 175 11th grade students found that 70 texted while driving. Assume Population 1 is defined as 12th-grade drivers and Population 2 is defined as 11th

grade drivers. What is the test statistic for this hypothesis test?

A.

2.29

B.

−1.73

C.

−2.47

D.

1.06

Answer 1

option A is correct

Answer 2

Answer:

Test Statistic: $\boxed{{\displaystyle A\mathrm{.}2.29}}$

Steps:

1. Sample Proportions:

• ${\widehat{p}}_1=\frac{84}{160}=0.525$ (12th grade).

• ${\widehat{p}}_2=\frac{70}{175}=0.400$ (11th grade).

2. Pooled Proportion ($\widehat{p}$):

   $$\widehat{p}=\frac{84+70}{160+175}=\frac{154}{335}\approx 0.460$$

3. Test Statistic ($z$):

   $$z=\frac{{\widehat{p}}_1-{\widehat{p}}_2}{\sqrt{\widehat{p}(1-\widehat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}=\frac{0.525-0.400}{\sqrt{0.460\times 0.540(\frac{1}{160}+\frac{1}{175})}}\approx 2.29$$

Conclusion: The test statistic matches option A (2.29).