An insurance company would like to test the hypothesis that a difference exists

Question

An insurance company would like to test the hypothesis that a difference exists in the proportion of students in

12th grade who text while driving when compared to the proportion of 11th grade drivers who text. A random sample of 160 12th grader 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. Using = 0.05, determine the critical value for this hypothesis test.

a) 1.645

b) 1.96

c) 2.33

d) 2.05

what is the p-value?

a) 0.1850

b) 0.0220

c) 0.0418

d) 0.1610

Explanation / Answer

1.

An insurance company would like to test the hypothesis that a DIFFERENCE exists in the proportion of students in 12th grade who text while driving when compared to the proportion of 11th grade drivers who text.

Thus, it is a two tailed test.

Hence, for alpha = 0.05, two tailed, the critical value is, by table/technology,

OPTION B: 1.96 [ANSWER]

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2.

Formulating the hypotheses          
Ho: p1 - p2   =   0  
Ha: p1 - p2   =/=   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.525      
p2 = x2/n2 =    0.4      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.054129681      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.31      
          
          
Also, the p value is          
          
P =    0.0220 [ANSWER, B]      
          

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