Read the following scenario completely and notice that the researchers desire a hypothesis test. After having read the entire scenario and considered all the steps necessary to obtain the desired hypothesis test answer questions 41-46. The reputations of many businesses can be severely affected by shipments of manufactured lots that contain defective items. To this point, a manufacturer has been able to maintain and advertise a 7% damaged goods rate in their past shipments. A client that repeatedly orders lots from this manufacturer isn’t so sure the 7% rate is accurate anymore because they are noticing more damaged goods in their orders. This client decides to test the “7% advertising claim” and is able to examine 632 recently shipped products from the manufacturer. Among this group of recently shipped items, 62 of them were damaged. 41.
The parameter being investigated in this problem is a) the fraction of damaged good being sent currently to the client b) all of the shipments being currently sent to the client c) the 7% of shipments being sent to the client that have damage out of the 632 d) the advertising claim e) the 62 damaged items that were sent to the client on their recent order 42.
What are the proper null and alternative hypotheses for this problem? a) 𝐻𝑂:𝑝 > .07 𝐻𝐴:𝑝 = .07
c) 𝐻𝑂:𝑝 = .07 𝐻𝐴:𝑝= .07
e) 𝐻𝑂:𝑝 > .07 𝐻𝐴:𝑝> .07 43.
b) 𝐻𝑂:𝑝 = .7 𝐻𝐴:𝑝 > .7 d) 𝐻𝑂:𝑝 = .07 𝐻𝐴:𝑝 > .07 The value of the proper z-statistic for this hypothesis test is a) .0981
44.
b) .0028
c) 2.77
d) 69.604 e) 6.897 The p-value picture that would be drawn for this problem a) shades area to the left since the z-chart gives you the area to the left of a particular value b) shades all of the area in the middle 95% of the curve c) shades the area to the right, which is the area in a small tail d) shades all the area to the right of .07 since this matches the alternative hypothesis e) shades the area to the left of the calculated z-value since all complement rule problems shade to the left 45.
a) .9972
The actual p-value for the hypothesis test in this problem is b) .0277
c) .0028
d) .0981
e) less than .0001 46.
The overall conclusion to the hypothesis test performed in this problem is a) We have insufficient evidence of false advertising. The percentage of damaged goods has not significantly increased over the stated 7% value. b) The client is mistaken. The fraction of damaged goods being sent to them is actually significantly less than the 7% historical claim. c) We have sufficient evidence of false advertising. The data in the sample suggest that the fraction of damaged goods recently being sent to the client has increased above the 7% stated rate. d) The sample contains over 7% damaged goods. But this fraction is not significantly high enough to claim that the business is no longer meeting its 7% advertising rate. e) the fraction of damaged goods being shipped to all clients in all samples at the present time is essentially 10% now. The advertising claim needs updating.