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?

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:  

Alternative hypothesis:  

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.

Step-by-step explanation:

Data given and notation  

represent the sample mean    

represent the sample standard deviation

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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:  

Alternative hypothesis:  

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.

well, because the $0.25 is an added cost depending on how many minutes, the answer would be y = 30 + 0.25x.