Question

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Answer 1

Solution:-

a)

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 one-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 = 0.1122
SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] }
SE = 0.01810065
z = (p₁ - p₂) / SE

z = - 1.97

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 - 1.97.

Thus, the P-value = 0.039.

Interpret results. Since the P-value (0.039) is less than the significance level (0.05), we have to reject the null hypothesis.

(D) Reject H0, there is sufficient evidence to support the claim that commercial truck owners violate laws requiring front licence plate at a higher rate than owners of passenger cars.

b)

C.I = (p1 - P2) 2a/2 1 Pi(1-P) ni P2(1 - P2) n2

C.I = (0.10721 - 0.14286) + 1.96*0.0181

C.I = 0.03565 + 0.035476

C.I = (0.0002, 0.0711)

Because the confidence interval limits does not contain 0, there is a significant difference between the two proportions. There is sufficient evidence to support the claim that commercial trucks owner violate laws requiring front licence plates at higher rate than owners of passenger cars.