In Massachusetts, the NHTSA (National Highway Safety Administration) instituted

Question

In Massachusetts, the NHTSA (National Highway Safety Administration) instituted an observational study to assess various driving habits, especially pertaining to the use of seatbelts in 2007. By filming automobiles as they passed under a particular bridge, they were able to record various information per automobile. This particular assessment focused on male drivers, whether he wore a seat belt or not, and whether someone was accompanying him in the automobile (male or female). While the methodology was very complex, the results can be considered suitable random samples. The following data was obtained. Among 255 male drivers that were observed with a female passenger, 168 used their seatbelt (65.9%). Among 310 male drivers that were observed with a male passenger, 160 used their seatbelt (51.6%). Let p1 represent the population proportion of all male drivers who wear seatbelts in the presence of a female passenger, and p2 represent the population proportion of all male drivers who wear seatbelts in the presence a male passenger. The Director of the NHTSA asks that these results be used to test the hypotheses H0: p1 = p2 versus Ha: p1 > p2 using a level of significance of 0.05. The Director's theory is that male drivers are more likely to use seatbelts in the presence of a woman as compared to a man.

Question 6 Subquestions

6.a

1 point(s)

If the null hypothesis is true, which of the following must be our best estimate of the common proportion p?

0.143

0.5805

0.5875

1.175

6.b

2 point(s)

Calculate the value of the test statistic.

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6.c

3 point(s)

Provide a complete sketch of the p-value for this test and the corresponding value of the p-value.

No answer entered. Click above to enter an answer.

6.d

1 point(s)

The decision is to reject the null hypothesis at the 5% level. Which of the following is the appropriate conclusion in the context of the problem?

There is insufficient evidence to conclude the population proportion of men who wear a seat belt with a female passenger is greater than when the passenger is male.

There is sufficient evidence to conclude the population proportion of men who wear a seat belt with a female passenger is greater than when the passenger is male.

Explanation / Answer

Solution:-

x1 = 168, n1 = 255, p1 = 0.659

x2 = 160, n2 = 310, p2 = 0.516

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2

Alternative hypothesis: P1 > P2

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.5805

S.E = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

S.E = 0.041718

z = (p1 - p2) / SE

z = 3.4278

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 3.43. We use the Normal Distribution Calculator to find P(z < - 3.43) = 0.000304. Thus, the P-value = 0.000304

Interpret results. Since the P- value (0.000304) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:There is sufficient evidence to conclude the population proportion of men who wear a seat belt with a female passenger is greater than when the passenger is male.

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