Question

Two different machines, A and B, are used to perform the same task in an industry. It is suspected that machine A has an average time to perform the task greater than machine B. To verify this suspicion, a random sample of 35 times from machine A and 32 times from machine B was collected, and the results found were:

Machine	Average	Standard Deviation
A	28,87	1,05
B	27,89	1,85

(a) What does the data allow to conclude about the suspicion formulated, considering α = 1%?
(b) Are the assumptions necessary to perform this test met?

Answer 1

a)

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a right-tailed test, so the p-value is given by:

Since p-value is less than 0.01, so we have sufficient evidence to reject the null hypothesis H0.

Thus we can conclude that .

b)

Since the samples are large enough (greater than 30), so the assumptions (of normality of the population) aren't necessary.