Question

1. A study of the accuracy of fast food drive-through orders, one restaurant had 37 orders that were not accurate among 333 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. a. Identify the null hypotheses and alternate hypotheses. Ho: H1: b. Find the test statistics equation and value. c. Find the P value for this hypothesis test. d. State the conclusion about Ho and H1. Why do we accept/reject Ho and accept/reject H1?

Answer 1

Solution:

Claim : To test whether that the rate of inaccurate orders is equal to 10% or not

a) Hypothesis : Ho:p=0.10
H1:p ≠ 0.10
Two tailed test
Given that
number of orders that were not accurate x = 37
sample size n = 333
sample proportion p̂ = x/n = 37/333 = 0.1111
α =0.05
b) Test statistic z = p̂ - p/sqrt(p(1-p)/n)
= 0.1111-0.10/sqrt(0.10(1-0.10)/333)
= 0.675

c) p-value : By using excel command we get the exact p-value
Excel command is =NORMSDIST(z)
=NORMSDIST(0.675)
= 0.7502

p-value : P(Z > 0.675) = 2 * 0.7502 = 1.5004

Decision Rule: p-value > alpha, We Fail to reject Ho

d) Conclusion : There is sufficient evidence to conclude that the rate of inaccurate orders is NOT equal to 10%