‘A carpet company advertises that it will deliver your carpet within 15 days of

Question

‘A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken.” The average delivery time in the sample was 16.6 days. Assume the population standard deviation is known to be 5.6 days. Answer questions:

1. What is the cut-off point at alpha = .05?

2. What is the cut-off point if Type I error is 1%?

3. Would you reject the Null at 5% level of significance?

4. Would you reject the Null at 1% level of significance?

5. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .01?

6. If suppose the true delivery time for the population is 17 days. What is the Type II error at Alpha = .05? 0.1949

19.62%

Yes

16.864

43.25%

16.316

No

Explanation / Answer

1) here std error of mean =std deviation/(n)1/2 =0.8

fo0r 0.05 level ; critical z =1.645

therefore cutoff value =mean +z*std deviation =15+1.645*0.8=16.316

2)for 0.01 level; z=2.326

therefore cutoff value =mean +z*std deviation =15+2.33*0.8=16.864

3)Yes as cutoff value is lower then 16.6

4) No as cutoff value is higher then 16.6

5)Type II error =P(X<16.864)=P(Z<(16.864-17)/0.8)=P(Z<-0.17)=43.25%

6)Type II error =P(X<16.864)=P(Z<(16.316-17)/0.8)=P(Z<-0.855)=19.62%

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