Two suppliers manufacture a plastic gear used in a laser printer. The impact str
ID: 2949384 • Letter: T
Question
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 Xi 289.30 and s 22.5, and another random sample of 16 gears from the second supplier results in X2 = 322.10 and s2-21. Use only Table V of Appendix A. 005, and (a) Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use ? assume that both populations are normally distributed but the variances are not equal Round your answer to 4 decimal places. P-valueExplanation / Answer
a)
Hypothesis:
H0 : mu1 =mu2
Ha : mu1 < mu2
test statistics:
t = (x2 -x1)/sqrt(s2^2/n2 +s1^2/n1)
= (322.1-289.3)/sqrt(21^2/16 + 22.5^2/16)
= 4.2629
p value = .0011
0.0001 < 0.0011 < 0.05
Reject the null hypothesis
b)
Hypothesis:
H0 : mu1 - mu2 = 25
Ha : mu1 - mu2 < 25
test statistics:
t = ((x2 -x1)- 25)/sqrt(s2^2/n2 +s1^2/n1)
= ((322.1-289.3)- 25)/sqrt(21^2/16 + 22.5^2/16)
= 1.0137
p value = .1685
0.05 < 0.1685 < 0.2
Do not Reject the null hypothesis
c)
t value at 95% = 2.2622
CI = (x1-x2) +/- t *sqrt(s1^2/n1 +s2^2/n2)
= (322.1-289.3) +/- 2.2622*sqrt(21^2/16 + 22.5^2/16)
= (15.394,50.206)
15.394 < mu2 -mu1 < 50.206
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