Question

Chicken Delight claims that 91% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 90 orders revealed that 81 were delivered within the promised time. At the 0.10 significance level, can we conclude that less than 91% of the orders are delivered in less than 10 minutes?

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

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.)

What is your decision regarding the null hypothesis?

Answer 1

Null hypothesis

H0 : P = 0.91

Alternative hypothesis

H1: P <0.91

We have for given example,

Population proportion value is =0.91

x=81

n=90

Level of significance = 0.1

One-tailed Test (lower)

Lower Critical Value -1.28

Decision rule : Reject H0 if Z calculated < -1.28

Estimate for sample proportion = 0.9

Z test statistic formula for proportion

Z test statistic =-0.33

p-value 0.3701

Decision Do not reject H0.

Conclusion: We do not have sufficient evidence at to say that,  less than 91% of the orders are delivered in less than 10 minutes