Question

Chicken Delight claims that 90% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 90 orders revealed that 80 were delivered within the promised time. At the 0.01 significance level, can we conclude that less than 90% of the orders are delivered in less than 10 minutes?

Answer 1

Answer with explanation:

Let p be the population proportion of orders are delivered within 10 minutes of the time the order is placed.

Then according to the claim we have ,

$H_0:p=0.90\\\\ H_a:p\neq0.90$

Since the alternative hypothesis is two-tailed so the hypothesis test is a  two-tailed test.

For sample ,

n = 90

Proportion of orders are delivered within 10 minutes of the time the order is placed=$\hat{p}=\dfrac{80}{90}\approx0.89$

Test statistics for population proportion :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\=\dfrac{0.89-0.90}{\sqrt{\dfrac{0.90(0.10)}{90}}}\approx-0.32$

The p-value : $2(z>-0.32)=0.7489683\approx0.75$ [By using standard normal distribution table]

Since the p-value is greater that the significance level (0.01), so we do not reject the null hypothesis.

Hence, we conclude that we have enough evidence to support the claim that 90% of its orders are delivered within 10 minutes of the time the order is placed.