Question

In a study of Wendy's drive through orders, it was found that 264 orders were accurate and 54 orders were not accurate. For Burger King 329 orders were found to be accurate while 33 were not accurate. Use a 0.05 significance level to test that hypothesis. Identify the null and alternative hypothesis, test statistic, P-value or critical value, state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim (show all of your work under each appropriately labeled step)

Answer 1

Answer:

Given,

sample proportion = p1 = x1/n1 = 264/318 = 0.8302

p2 = x2/n2 = 329/362 = 0.9088

Now,

p = (x1+x2)/(n1+n2)

substitute values

= (264 + 329)/(318 + 362)

= 0.8721

Ho : p1 = p2

Ha : p1 != p2

test statistic z = (p1 - p2)/sqrt(pq(1/n1+1/n2))

substitute values

= (0.8302 - 0.9088)/sqrt(0.8721(1-0.8721)(1/318+1/362))

= - 3.062

P value = 2*P(z < -3.062)

= 0.0021986 [since from z table] two tailed

= 0.0022

Here we observe that, p value < alpha, so we reject Ho. So we have sufficient evidence.