Question

You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined µ1 and process 2 has a mean defined as µ2 . the null and alternative hypotheses are as follows:

H0 = µ1- µ2 = 0

H1 = µ1- µ2 > 0

Using a random sample of 25 paired observations, the sample means are 50 and 60 for population 1 and 2 respectively, test the alternative when the level of significance is 0.05 and the sample standard deviation of the difference is 20.

Answer 1

Hypothesis:

H0 : µ1- µ2 = 0

H1 : µ1- µ2 < 0 ( we have to check µ1- µ2 < 0 not µ1- µ2 > 0 , because µ1 is less than µ2 ).

We use paired sample t test for testing above hypothesis.

Test statistic,

=

Degrees of freedom = n-1 = 24

Critical value = = 1.711

Since absolute value of test statistic is greater than critical value, we reject null hypothesis and conclude that µ1 is less than µ2.