# T-Test with two samples with different variance

- Author:
- Linda Fahlberg-Stojanovska

- Topic:
- Statistics, Variance

10-22 (3rd edition) Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in xbar1=290 and sig1=12, while another random sample of 16 gears from the second supplier results in xbar2=321 and sig2=22. (a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use alpha=0.05 and assume that the variances are not equal. (b) What is the p-value for this test? (c) Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).

What is the sample claim H1 in (a)? What is H0?
What is the sample claim H1 in (c)? What is H0?
Using alpha=0.05, for what amount of foot-pounds could we claim that the mean impact strength of gears from supplier 2 is higher?
What changes using alpha=0.025?
Source: Source of materials: Applied statistics and probability for engineers, 3rd ed., Chapter 10, D. Montgomery, G.Runger, 2010, 978-0470053041, Wiley & Sons.