Question

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 400 n2 = 500 Number of accidents = 190 Number of accidents = 150 Do people under the age of 18 get into significantly more accidents? Use a = 1%. "While I hope you have an appropriate null and alternative in mind while running through this hypothesis test, for today I will not be asking you what that is. Find the pooled proportion: Round to three decimal places. Find the correct test statistic. Round to three decimal places. Find the p-value: Write the conclusion in context: There (choose one: is/is not) enough evidence to suggest that people under the age of 18 get into significantly more accidents.

Answer 1

For sample 1, we have that the sample size is N1 = 400, the number of favorable cases is X1 = 190, so then the sample proportion is pi = X 190 = 0.475 400 For sample 2, we have that the sample size is N2 = 500, the number of favorable cases is X2 = 150, so then the sample proportion is P2 = 150 = 0.3 500 Ni+N2 The value of the pooled proportion is computed as = 190-150 400-500 = 0.3778 Also, the given significance level is a = 0.01. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p1 = P2 Ha: p1 > P2 This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the critical value for a right-tailed test is ze = 2.33. The rejection region for this right-tailed test is R = {z:z > 2.33} (3) Test Statistics The Z-statistic is computed as follows: Z = P1 - P2 Vp(1 - 7) (1/n1 +1/n2) 0.475 – 0.3 0.3778 . (1 -0.3778)(1/400 + 1/500) = 5.38 (4) Decision about the null hypothesis Since it is observed that z = 5.381 > ze = 2.33, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0, and since p= 0 <0.01, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1 is greater than p2 at the 0.01 significance level.

pooled proportion is 0.37 8

test statistic is 5.381

p value is 0.000

there is enough evidence to suggest that people under the age of 18 get into significantly more accidents.

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