Question

In a study of the accuracy of fast food drive-through orders, one restaurant had 37 orders that were not accurate among 301 orders observed. Use a 0.01 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable? Identify the test statistic for this hypothesis test. ( Round to two decimal places as needed.)

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 = 37 / 301 = 0.1229

P₀ = 0.10

1 - P₀ = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1229 / [(0.10 * 0.90) / 301]

= 1.326

P(z > 1.326) = 1 - P(z < 1.326) = 0.0924

P-value = 0.1848

= 0.01

P-value >

Fail to reject the null hypothesis .

the accuracy rate does not appear to be acceptable .