Question

XYZ Machining Company produces metal parts of a particular type for a specialized industry. Recently they purchased a newer machine to augment the one they had been using. A random sample of 1000 parts manufactured by the old machine showed 47 were defective, while 1000 parts manufactured by the newer machine had 23 which were defective. Test the hypothesis that the new machine produces fewer defective parts. Use a 1% significance level. Give the null and alternate hypotheses and the distribution that will be used for the test. Comment on the required conditions and any assumptions that must be made. Give the test statistic and p-value and use a complete sentence to explain your conclusion.

Answer 1

The hypothesis being tested is:

H0: p1 = p2

Ha: p1 > p2

p1	p2	pc
0.047	0.023	0.035	p (as decimal)
47/1000	23/1000	70/2000	p (as fraction)
47.	23.	70.	X
1000	1000	2000	n
	0.024	difference
	0.	hypothesized difference
	0.0082	std. error
	2.92	z
	.0017	p-value (one-tailed, upper)

The p-value is 0.0017.

Since the p-value (0.0017) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that the new machine produces fewer defective parts.