Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Statistics and Probability Expert

problem 1: A statistician is investigating the 'home ground' e ect and is studying 20 football games, of which 14 were won by the home team and 6 by the visitors. Thus the game is a Bernoulli trial with a home win counted as a 'success'. The R idiom is:

games <- c(14,6)

because 14 games were wins for the home side and 6 were won by the visitors.

a) If the games are independent, what distribution speci es the number of home wins?

b) What is a sensible null hypothesis to use in this context?

c) Using chisq.test(games), or otherwise, give a p-value for the observation.

d) Interpret your p-value in such a way that a football commentator (who is not a statistician) would understand.

e) NB: harder. Bearing in mind the precise de nition of a p-value [that is, the probability, if the null is true, of obtaining our observation or one more extreme], and the fact that in this context 'more extreme' means 'more home wins' [that is, 14 or more home wins], use dbinom() to find out a p-value for our observation.

problem 2: You will recall the function pnorm() from lectures. Using this, or otherwise, find outd the probability of a standard Gaussian random variable exceeding 1.3.

Using table(), or otherwise, verify your result numerically. You may fi nd a sketch helpful here.

problem 3: A scientist measures the temperature of melting platinum using a new type of thermometer. The temperature of the metal is known to be exactly 1768.3 centigrade. The measurements are as follows:

c(1770.1, 1771.1, 1769.19, 1769.5, 1767.32, 1768.67, 1768.22)

a) What is the mean of these observations?

b) In the context of hypothesis testing, and bearing in mind that it is not known whether the new thermometer overpredicts or underpredicts temperature, is a one-sided or two-sided test indicated? Justify your answer.

c) Conduct a Student t-test for the hypothesis that the mean of the temperatures is 1768.3 (you may use the mu argument of t.test() here). State whether the observations are signi cantly di erent from the known value.

d) Interpret the result of the statistical test in a way that the scientist, who is not a statistician, could understand.

e) Harder. Under what circumstances would a one-sided test be appropriate?

problem 4: A medical researcher has 100 bone cancer patients in a study. Each patient's condition is one of six types, type "A" to type "F". The 100 patients split as follows:

x <- c(11, 25, 10, 21, 16, 17)

Thus there are 11 patients with condition "A", 25 patients with "B", and so on.

Using chisq.test(), or otherwise, test the null hypothesis that the six conditions are equally likely; report your p-value.

Is there evidence that the conditions are not equally probable? Interpret your nding in such a way that a busy oncologist, who is not a statisician, could understand.

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M91468

Have any Question? 


Related Questions in Statistics and Probability

Kindergarten children have heights that are approximately

Kindergarten children have heights that are approximately normally distributed about a mean of 38.8 inches and a standard deviation of 1.5 inches. If a random sample of 21 is taken, what is the probability that the sampl ...

A recent report suggested that older people think more

A recent report suggested that older people think more slowly than younger people because they have more information stored in their brains. Because WeStudyEverything wasn't sure regarding the source of the study, they d ...

A parcel of land purchased by clean energy inc is estimated

A parcel of land purchased by Clean Energy, Inc. is estimated to contain 15.25 million tons of anthracite coal. The purchase price was $10,850,000, startup costs were $3,411,000, and the residual value is $1,464,000. If ...

Twenty years ago 40 children were born in the same hospital

Twenty years ago 40 children were born in the same hospital in Denmark. Researchers classified the children by whether or not they were breast-fed for at least 3 months. They were interested in whether breast-feeding ten ...

Research objectives to explore correlations between reward

Research Objectives To explore correlations between reward systems and team work attributes in the Saudi Arabian bank sector To explore relationships between reward systems and team work effectiveness in the Saudi Arabia ...

Use the inverse transform method to generate a sample of

Use the inverse transform method to generate a sample of the exponential distribution with parameter θ, which is given by its density             1/θe -x/θ   for x ≥ 0 f(x) =             0             for x where θ is a ...

At stats high there is a difficult exam that every junior

At Stats High, there is a difficult exam that every junior takes. Over the last 5 years, the exam results are normally distributed with a mean of 35% and a standard deviation of 7%. If your friend takes the exam and rece ...

Calculated the correlation between outside temperature and

Calculated the correlation between outside temperature and class attendance. The regression equation for the data in that exercise is Attendance = 114.35 - .61 (temperature). Imagine that the weather forecaster predicts ...

Assume the sweatshirt test scores are normally distributed

Assume the sweatshirt test scores are normally distributed with a mean of 500 and a standard deviation of 100. (a) Consider all random samples of 100 test scores. What is the standard deviation of the sample means? (b) W ...

44nbspof a certain countrys voters think that it is too

44% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is ( ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro