Question

A local pizza store knows the mean amount of time it takes them to deliver an order is 45 minutes after the order is placed. The manager has a new system for processing delivery orders, and they want to test if it changes the mean delivery time. They take a sample of delivery orders and find their mean delivery time is 48 minutes and the standard deviation is 10 minutes. Significance level (a=0.05)

Is there any difference of the pizzas delivery time between the sample average and company's claim?

Answer 1

Yes, because 0.023<0.05

Answer 2

We need to conduct a hypothesis in order to check if the true mean is different from 45(alternative hypothesis), and then the system of hypothesis would be:

Null hypothesis:
`\mu =45`

Alternative hypothesis:
`\mu \\eq 45`

Since we don't know the sample size we can't calculate the statistic and the only thing that we can do is create the sytem of hypothesis.

Explanation:

Data given and notation

`\bar X=48` represent the sample mean

`s=10` represent the sample standard deviation

`n` sample size

`\mu_o =45` represent the value that we want to test

`\alpha=0.05` represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

`p_v` represent the p value for the test (variable of interest)

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is different from 45(alternative hypothesis), and then the system of hypothesis would be:

Null hypothesis:
`\mu =45`

Alternative hypothesis:
`\mu \\eq 45`

Since we don't know the sample size we can't calculate the statistic and the only thing that we can do is create the sytem of hypothesis.