Question

2. The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population mean is 3.5 minutes and the population standard deviation is known to be 0.5 minutes. We would like to know if there is evidence of a change in average check out time. Explain in the context of this question what a type 1 error would be: (you do not need to solve the entire problem, just explain the error in the context of the problem) 5 points.

Answer 1

Answer)

Null hypothesis Ho : u = 3.5

Alternate hypothesis Ha : u not equal to 3.5

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (3.1-3.5)/(0.5/√100) = -8

As the population s.d is known here we can use standard normal z table to estimate the p-value

From z table, P(z<-8) = 0

As the test is two tailed

P-value = 2*0 = 0

As the obtained p-value is extremely less we reject the null hypothesis

So we have enough evidence to support the claim that there is a change in the mean

Type 1 error means rejection of true null hypothesis

So if we will reject the null hypothesis that u is 3.5 but infact it is 3.5 then we will commit type 1 error