🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →
Log in
Statistics
1
answer
0
watching
20
views

Assigned: Monday, Jan. 27, 2020 – Due: Sunday, Feb. 9, 2020 (Beginning of Class) PROBLEM 1 State every possible event in the sample space S = (a, b,c).

Watch
1
answer
0
watching
20
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Unlock all answers

Get 1 free homework help answer.
Get unlimited access
Already have an account? Log in
Share

Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space   Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

                                        Y=0                                Y=1

X=0    
X=1    

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?

Problem 1 (2 points). Every month a clothing store conducts an inventory and calculates the losses due to theft. The store would like to reduce these losses and is considering two methods to do so: the first is to hire a security guard and the second is to install cameras. The manager of the store has conducted the experiment: During the first 6 months he hired a security guard (method 1) and during the next 6 months he installed cameras (method 2). The monthly losses were reported as follows:

Security guard 350 289 407 398 470 259 Cameras 488 301 276 380 421 425

a/ Test with a=0.05 to determine whether there is enough evidence to conclude that expected monthly loss when installing cameras differs from 382. b/Since the cameras are cheaper than the guard, the manager would prefer to install the cameras unless there was enough evidence to infer that the guard was better. Conduct a hypothesis testing to advise what the manager should do? (Assuming equal variances and using a= 0.05)

Problem 2 (2 points). A supermarket chain performed a survey to help determine desirable locations for its new stores. The management of the chain wanted to know whether a linear relationship exists between weekly take home pay (s) and weekly food expenditures (y). A random sample of eight households produced the data shown in the following table Household 1 3 7 8 2 4 5 6 550 450 560 340 510 710 470 660

170 100 160 80 120 190 140 140 Y

a/ Find the least square regression line.

b/Perform the test Ho: Bi=0, H4: B10 (using a = 0.05) to determine whether there is enough evidence to infer that a linear relationship exists between weekly take home pay (s) and weekly food expenditures (y).

A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of α = 0.05 is chosen.

    1. (a)  State hypotheses appropriate to the research question.
    2. (b)  Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
    3. (c)  Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
    4. (d)  Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
    5. (e)  Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?

Weekly leaderboard

Home
Homework Help 3,900,000
Statistics 10,000
Start filling in the gaps now
Log in