Statistics Question

Homework 8 STAT 516: Statistics II

Spring, 2018

NOTE This is due at the start of class on Thursday April 12th. If it is not turned in within the first 5 minutes of lecture, it will be considered late and subject to penalty.

1–5) From the textbook, problems: 10.69 (parts a,c,d), 10.78, 10.81, 10.91, 10.99

6) Suppose that the manufacturer of a particular light bulb claims their light bulb has an aver- age lifetime of 600 hours. A consumer protection bureau buys 10 light bulbs and finds the following lifetimes:

x = {831, 90, 473, 580, 94, 445, 35, 818, 500, 509}. Is there evidence at α = 0.05 to suggest the manufacturer is over-inflating the light bulbs average lifetimes? Using the Wilcoxon signed-rank test and the attached Wilcoxon table, carry out your testing procedure.

7) The manufacturer in question (6) claims to have created a better light bulb! They claim this new light bulb has a lifetime of 800 hours. A consumer protection bureau buys 10 of these new light bulbs (in addition to the ten light bulbs from question 6) and finds the following lifetimes:

y = {572, 623, 444, 422, 768, 966, 566, 788, 426, 923}. Compute the Wilcoxon rank-sum test statistic for testing whether the new light bulb has a longer lifetime. Using the following R output, is there evidence at α = 0.05 to suggest the manufacturer created a longer lasting light bulb?

1

Note that the table provides wα such that wα is the largest value for which P(W < wα) ≤ α