Question

A consumer advocacy group wants to determine whether there is a difference between the proportions of the two leading automobile models that need major repairs (more than $500) within two years of their purchase. A sample of 400 two-year owners of model 1 is contacted, and a sample of 500 two-year owners of model 2 is contacted. The numbers x1 and x2 of owners who report that their cars needed major repairs within the first two years are 53 and 78, respectively. What is the p-value of the appropriate test of hypotheses

Answer 1

Answer:

The answer is "0.3206".

Step-by-step explanation:

$H_0: p_1 = p_2\\\\H_a: p_1 \neq p_2\\\\\hat{p_1} = \frac{X_1}{N_1} = \frac{53}{400} = 0.1325\\\\\hat{p_1}= \frac{X_2}{N_2} = \frac{78}{500}= 0.156\\\\\hat{p} = \frac{(X_1 + X_2)}{(N_1 + N_2)} = \frac{(53+78)}{(400+500)} = 0.1456$

Testing statistic:

$z = \frac{(\hat{p_1}- \hat{p_2})}{\sqrt{(\hat{p} \times (1-\hat{p}) \times (\frac{1}{N_1} + \frac{1}{N_2}))}}$

$=\frac{(0.1325-0.156)}{\sqrt{(0.1456\times (1-0.1456)\times (\frac{1}{400} + \frac{1}{500}))}}\\\\ = -0.99$

Calculating the P-value Approach

$\text{P-value}= 0.3206$