A 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.
a. Select the null and the alternative hypotheses to test the policy analyst's objective.
A. He : p 0.82; Ha: p +8.82
B. He: P 8.82; HA: P8.82
b-1. 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? (Negative values should be Indicated by a minus sign. Round Intermedlete calculatlons to at least 4 decimal places and final answer to 2 declmal places.)
b-2. Find the p-value.
a. p-value<0.01
b. 0.01 s p-value<0.025
c. 0.025 s p-value d. 0.05 sp-value<0.10
e. p-value z 0.10
c-1. At a 0.05, do you reject the null hypothesis?
A. Yes, since the p-value is greater than significance level.
B. Yes, since the p-value is smaller than significance level.
C. No, since the p-value is greater than significance level.
D. No, since the p-value is smaller than significance level.
c-2. What is the conclusion?
A. The law has been effective since the pvalue is less than the significance level.
B. The law has not been effective since the pvalue is less than the significance level.
C. The law has been effective since the p-value is greater than the significance level.
D. The law has not been effective since the p-value is greater than the significance level.

Answer:

a)Null hypothesis; H0: p = 0.82

Alternative hypothesis; Ha: p < 0.82

b-1) test statistic = -2.57

b-2)The p-value = 0.00545

c-1)Option B: Yes, we will reject the null hypothesis since the p-value is smaller than significance level.

c-2) Option A: The law has been effective since the p-value is less than the significance level

Step-by-step explanation:

A) We are given population mean as 82% = 0.8.l2

Thus defining the hypothesis, we have;

Null hypothesis; H0: p = 0.82

Alternative hypothesis; Ha: p < 0.82

b-1) We are told that a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. Thus; p^ = 150/200 = 0.75

Test statistic is given by the formula;

t = (p^ - p)/(√(p(1 - p)/n)

t = (0.75 - 0.82)/√(0.82(1 - 0.82)/200)

t = -0.07/0.0272

t = -2.57

b-2) From online p-value from t-value attached using; t = -2.57, significance level = 0.05, one tail distribution, and DF = 200 - 1 = 199, we have;

The p-value = 0.00545

c-1) Option B: Yes, we will reject the null hypothesis since the p-value is smaller than significance level.

C-2) We will conclude that;

The law has been effective since the pvalue is less than the significance level.

You can perform the t test for single mean to test the hypothesis.

The solutions are:

A: The null hypothesis: [tex]H_0: p= 0.82\\[/tex]

The alternate hypothesis: [tex]H_1: p < 0.82[/tex]

B: 1)  The value of t statistic is -2.58

2) The p value is 0.0053

C: 1)  Yes, since the p-value is smaller than significance level.

2)  The law has been effective since the p-value is less than the significance level.

We take null hypothesis for events as if nothing changed. So we will  the changed population mean to be same as before. Or  [tex]H_0: p = 0.82\\[/tex]

And thus, the alternate hypothesis will be that the mean is decreased than 82% due to the new law, thus,

The alternate hypothesis: [tex]H_1: p < 0.82[/tex]

Solving for all problems:

A) We take null hypothesis for events as if nothing changed. So we will  the changed population mean to be same as before. Or  [tex]H_0: p = 0.82\\[/tex]

And thus, the alternate hypothesis will be that the mean is decreased than 82% due to the new law, thus,

The alternate hypothesis: [tex]H_1: p < 0.82[/tex]

B) 1) The sample size = n = 200, the percentage of people using phone is: [tex]\dfrac{150 \tiems 100}{200} = 75\%[/tex] thus p' = 0.75

The value of t statistic is calculated as:

[tex]t = \dfrac{p' - p}{\sqrt{(p)(1-p)/n}}\\\\t = \dfrac{0.75 - 0.82}{\sqrt{0.82 \times 0.18 / 200}} = -2.577[/tex]

2) p value from t table at df = 200 -1  == 199, we have p value at t = -2.58

The p value is 0.0053

C) 1) since the obtained p value is less than the significance level 0.05, thus we  will reject the null hypothesis and accept the alternate hypothesis. Thus,

Yes, since the p-value is smaller than significance level.

2) Thus, the conclusion is:

The law has been effective since the p-value is less than the significance level.

The solutions are:

A: The null hypothesis: [tex]H_0: p= 0.82\\[/tex]

The alternate hypothesis: [tex]H_1: p < 0.82[/tex]

B: 1)  The value of t statistic is -2.58

2) The p value is 0.0053

C: 1)  Yes, since the p-value is smaller than significance level.

2)  The law has been effective since the p-value is less than the significance level.

Learn more about null and alternative hypothesis here:

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