Question

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 32 orders that were not accurate among 382 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable?

a. The test statistic for this hypothesis test is: __________________

b. The P-value for this hypothesis test is: __________________

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p 0.10

= x / n = 32 / 382 = 0.0838

P₀ = 0.10

1 - P₀ = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0838 - 0.10 / [(0.10 * 0.90) / 382]

= -1.057

Test statistic = -1.06

P(z < -1.06) = 0.1446

P-value = 0.2892

= 0.05

P-value >

Reject the null hypothesis .

The accuracy rate does not appear to be​ acceptable .