Question

In the study of the accuracy of fast food drive through orders, one restaurant had 40 orders that were not accurate among 307 orders observed. Use a 0.05 significance level to the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p 0.10

n = 307

x = 40

= x / n = 40 / 307 = 0.1303

P₀ = 0.10

1 - P₀ = 1 - 0.10 = 0.90

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1303 - 0.10/ [(0.10 * 0.90) / 307]

= 1.769

Test statistic = 1.769

P(z > 1.769) = 1 - P(z < 1.769) = 1 - 0.9616 = 0.0384

P-value = 2 * P(z > 1.769) = 2 * 0.0384 = 0.0768

= 0.05

P-value >

Fail to reject the null hypothesis .

The accuracy rate is not appear to be acceptable .