Question

A university library ordinarily has a complete shelf inventory done once every year. Because of new shelving rules instituted the previous year, the head librarian believes it may be possible to save money by postponing the inventory. The librarian decides to select at random 1000 books from the library's collection and have them searched in a preliminary manner. If evidence indicates strongly that the true proportion of misshelved or unlocatable books is less than.02, then the inventory will be postponed. Among 1000 books searched, 15 were misshelved or unlocatable. Test the relevant hypothesis and advise the librarian what to do (use a.05) (a) Do not reject Ho since -1.13 is not less than -1.64. The inventory should not be postponed. (b) Do not reject Ho since -1.13 is not less than -1.64. The inventory should be postponed. (c) Do not reject Ho since -1.13 is not less than -1.96. The inventory should not be postponed. (d) Do not reject Ho since -1.13 is not less than-1.96. The inventory should be postponed. (e) Do not reject Ho since -1.48 is not less than -1.64. The inventory should not be postponed. (Continuation of 13.) Find the p-value (a).5168 (b).0694 (c) .2584 (d).1292 (e).1883 (Continuation of 13.) If the true proportion of misshelved and lost books is actually 01, what is the probability that the inventory will be (unnecessarily) taken? (a).192 (b).176 (c).142 (d)9(e.103

Could you show the solution for the third question?. I understand the first two. The answer to the third is a)

Answer 1

Ans:

3)z cut off value=-1.64

sample proportion cut off value=0.02-1.64*SQRT(0.02*(1-0.02)/1000)=0.012739

when true proportion=0.01

z=(0.012739-0.01)/SQRT(0.01*(1-0.01)/1000)

z=0.87

P(type II error)=P(fail to reject H0/when H0 is false)=P(z>0.87)=0.192

Option a is correct(0.192)