Homework 4
mining代做 – 这是利用mining进行训练的代写, 对mining的流程进行训练解析, 涵盖了mining等方面
STAT 415
Due July 28, 2022
1
LetXequal the thickness of spearmint gum manufactured for vending machines. Assume that the distribution ofXisN(,^2 ). The target thickness is 7.5 hundredths of an inch. We shall test the null hypothesis, using ten observations.
(a) Define the test statistic and rejection region for an= 0.05 significance level test. Sketch a figure
illustrating this critical region.
(b) Calculate the value of the test statistic and state your decision clearly, using the followingn= 10
observations, randomly selected from the production line.
7.65 7.60 7.70 7.55 7.
7.55 7.40 7.40 7.50 7.
(c) Is our hypothesized mean of 0 = 7.50 contained in a 95% confidence interval for?
2
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people suffering from insomnia. After exa mining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observeY, the number for whom the drug dose induces sleep. We wish to test the hypothesisH 0 :p= 0. 8 vs.H 1 :p < 0 .8. Assume that the rejection region{y 12 }is used.
(a) In terms of this problem, what is a type I error?
(b) Find.
(c) In terms of this problem, what is a type II error?
(d) Find.
(e) Findwhenp= 0.6.
(f) Findwhenp= 0.4.
3
A bowl contains two red balls, two white balls, and a fifth ball that is either red or white. Letpdenote the probability of drawing a red ball from the bowl. We shall test the simple null hypothesisH 0 :p= 3/5 vs. H 1 :p= 2/5. Say we will draw four balls at random, one at a time and with replacement. LetXequal the number of red balls drawn.
(a) Define a rejection region for this test in terms ofX.
(b) For the rejection region youve defined, find the values ofand.
1
4
High airline occupancy rates on scheduled flights are essential for profitability. Suppose that a scheduled flight must average at least 60% occupancy to be profitable and that an examination of the occupancy rates for 120 10:00 A.M. flights from Atlanta to Dallas showed mean occupancy rate per flight of 58% and standard deviation 11%. Test to see if sufficient evidence exists to support a claim that the flight is unprofitable. Find the p-value associated with the test. What would you conclude if you wished to implement the test at the = .10 level?