Question

1. Dunder Mifflin recently expanded its supply to include not just paper, but also copiers (much to Pam’s delight). The expansion was a smashing success, with the copier production process producing defective parts only 0.8% of the time during the first year. Michael Scott believes that updates to the production technology have improved this process. He randomly selects 1000 parts and finds 6 defective parts. Do these data provide evidence at the 5% level that the process has improved?

(a) Give the appropriate hypotheses for this test and define any parameters used.

(b) List and verify conditions for the appropriate hypothesis test.

(c) Give the appropriate test statistic. Show formula, work, and value.

(d) Find the rejection region. Draw an appropriate picture, show work, and give the value to 2 places.

(e) What is your decision regarding the null hypothesis?

(f) What are your conclusions about this particular test?

(g) As regional co-manager of Dunder Mifflin, Jim suggests using the p-value approach to double check the study. Find the appropriate p-value. What would be your decision regarding the null hypothesis using this test instead of the rejection region approach? Does your conclusion change at all?

Answer 1

Answer:

Given,

Ho : p = 0.008

Ha : p != 0.008

Here the assumptions are sample drawn was normal distributed

consider,

p^ = x/n = 6/1000

= 0.006

test statistic z = (p^ - p)/sqrt(p(1-p)/n)

= (0.006 - 0.008)/sqrt(0.008(1-0.008)/1000)

z = - 0.71

Here at 5% siginificance level, z critical value is +/- 1.645

P value = 0.4777041 [since from z table]

= 0.0478

Here we observe that, p value > 0.05, so we fail to reject Ho.

So we don't have enough evidence.