A recent study by Allstate Insurance Co. finds that 82% of teenagers have used c
ID: 3396564 • Letter: A
Question
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
Explanation / Answer
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]