Question

The Acme Company manufactures large capacity Flash drives using two different manufacturing processes. The company is interested in determining if there is a significant difference in the average manufacturing time of the two processes. For Process #1, a sample of 28 items shows a sample mean of 9 minutes and a sample standard deviation of 3.5 minutes. For Process #2, a sample of 23 items shows a sample mean of 13 minutes and a sample standard deviation of 4.5 minutes. At a 5% level of significance, Test the claim of no difference in the average time for the two processes. What is your conclusion?

Answer 1

SOLUTION:

From given data,

For Process #1, a sample of 28 items shows a sample mean of 9 minutes and a sample standard deviation of 3.5 minutes.

For Process #2, a sample of 23 items shows a sample mean of 13 minutes and a sample standard deviation of 4.5 minutes. At a 5% level of significance.

Given as,

For Process #1:

= 9

= 3.5

= 28

For Process #2:

= 13

= 4.5

= 23

Formula for test statistic

test statistic = ( - ) /

= (9 - 13) /  

= -4 / 1.1480134

= -3.484279

level of significance is 5%

= 0.05

/2 = 0.05 / 2 = 0.025

Critical value = invt(0.025 ,df=22) = -2.074

conclusion

Since the test statistic is less than the critical value ,

you would reject the null hypothesis.

There is enough evidence at a 5% level of significance to conclude that there is difference in the manufacturing time.