A recent study by Allstate Insurance Co finds that 82 of tee

A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone. Use Table 1 and Table 2.

a. Select the null and the alternative hypotheses to test the policy analyst’s objective.

H0: p = 0.82; HA: p 0.82

H0: p 0.82; HA: p > 0.82

H0: p 0.82; HA: p < 0.82

b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round \"test statistic\" to 2 decimal places and \"p-value\" to 4 decimal places.)

Test statistic?

p-value ?

c. At = 0.05 has the law been effective? Yes/No

Test using the critical value approach with = 0.05.

d-1. Calculate the critical value. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

d-2. Interpret the results.

Reject H0/Do not reject H0

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.82
Ha:   p   <   0.82 [ANSWER, OPTION C]

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B)

As we see, the hypothesized po =   0.82      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.75      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.027166155      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.576735608   [ANSWER, TEST STATISTIC]  
  
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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.00498691   [ANSWER, P VALUE]

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C)

As P < 0.05, YES, THE LAW IS EFFECTIVE.

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d-1.

As this is a left tailed 0.05 level test,

zcrit - -1.65 [ANSWER]

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d-2.

As z < -1.65, we reject Ho. [ANSWER]