Question

Chicken Delight claims that 92% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 80 orders revealed that 70 were delivered within the promised time. At the 0.01 significance level, can we conclude that less than 92% of the orders are delivered in less than 10 minutes?

A.) What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

B.) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round the intermediate values and final answer to 2 decimal places.)

Answer 1

Solution:

Let   be the sample proportion.

= x/n = 70/80  = 0.875

Let p be the population proportion.

Null and alternative hypothesis are

H0 : p = 0.92

H1 : p < 0.92

A)

Left tailed test

Critical value is =   = -2.33

Decision Rule : Reject H₀ if z < -2.33

B)

The test statistic z is

z =   

=  (0.875 - 0.92)/[0.92*(1 - 0.92)/80]

= -1.48