Question

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 40 minutes. The owner has randomly selected 42 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 40 minutes. Suppose the P-value for the test was found to be 0.0281. State the correct conclusion based on each significance level.

Answer 1

The hypotheesis for the given test is :-

$\small H_0 : \mu \le 40$     (Null hypothesis)

$\small H_1 : \mu > 40$     (Alternate hypothesis)

p value is found to be 0.0281

Let $\small \alpha$ be the level of significance.

We know that,

$\small p\ value < \alpha \implies rejection \ of \ null \ hypothesis \\ \ p\ value > \alpha \implies accept \ the \ null\ hypothesis$

Note that,

Accept the null hypothesis means the average time spent on the deliveries does not exceed 40 minutes.

Reject the null hypothesis means the mean delivery time actually exceeds 40 minutes.

For $\small \alpha$ = 0.01 (1%), accept the null hypothesis.

For $\small \alpha$ = 0.02 (2%), accept the null hypothesis.

For $\small \alpha$ = 0.05 (5%), reject the null hypothesis.

i.e we come to the conclusion that, reject null hypothesis if significance level is greater than 2% (=0.02).