Question

A grinding machine will be qualified for a particular task if it can be shown to produce less than 8% defective parts. In a random sample of 300 parts, 12 were defective. On the basis of these data, is there sufficient evidence to suggest the machine is qualified? Use a 5% significance level.

(a) Define the parameter of interest for this situation.

(b) What are the hypotheses for this test?

(c) State and check the conditions needed to perform an appropriate hypothesis test.

(d) Using calculation by hand, what is the test statistic for this hypothesis test? Show work.

(e) Draw a picture representing the p-value for the hypothesis test.

(f) Find the p-value for the hypothesis test.

(g) What is your decision about the null hypotheses for this test and why is that your decision?

(h) Is there sufficient evidence to suggest the machine is qualified? Explain

Answer 1

Solution:

Part {a}

Let D denote percentage of defective items.

Then Parameter of interest is the percentage of defective items produced

Part {b}

The hypothesis of the test is:

H₀: D>0.08 vs H₁: D< or equal to 0.08

Part {c}

Since n=300, which is large we can approximate it to normal distribution.

Hence it is the condition for appropriate normal test

Part {d}

Hence we define

where H=12/300=0.04

n=300

Based on z value and for alpha =0.05 we obtain Z_(alpha), we reject the null hypothesis if Z> Z_(alpha).

Please note that, By HomeworkLib rule we need to answer only 4 sub parts