please answer all parts of the question (this is one big question) also please r
ID: 3263532 • Letter: P
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please answer all parts of the question (this is one big question) also please round proerly based on what the question asks: and bold all answers when done (make it so i can follow easily)
This Question: 1 pt 10 of 14 (0 complete) This Quiz: 14 pts possible An insurance company collects data on seat belt use among drivers in a country. Of 1700 drivers 30 years old 26% sa d that the buckle up whereas-33 of 300 drivers 55-64 years old said that they did. At the 10% significance level do the data suggest that there is a difference sea be us bet een ver 30 3 ears old and those 55-64? Let population 1 be drivers of age 30-39 and let population 2 be drivers of age 55-64. Use the two-proportions z-test to conduct the required hypothesis test. What are the hypotheses for this test? O A. Ho : p1 > p2, Ha: p1 =p2 OB. Ho: p1 = p2, Ha: p1Explanation / Answer
Solution:-
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
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 two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. 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) = [(0.26 * 1700) + (0.24 * 1800)] / (1700 + 1800) = 0.2497
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0.2497 * (1 - 0.2497) * ( 1/1700 + 1/1800 ) ] = 0.0146386
z = (p1 - p2) / SE = (0.26 - 0.24)/0.0146386 = 1.366
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 two-tailed test, the P-value is the probability that the z-score is less than -1.366 or greater than 1.366.
We use the Normal Distribution Calculator to find P-value
The P-Value is 0.171939.
The result is not significant at p < 0.10.
Interpret results. Since the P-value (0.171939) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Conclusion. Fail to reject null hypothesis. We have sufficient evidence to prove the claim.
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