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

Packages of sugar bags for sweeter sugar inc have an

Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 10 ounces and a standard deviation of 0.2 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly s ...

Consider a normal population with mu 47 and sigma 6

Consider a normal population with μ = 47 and σ = 6. Calculate the z-score for an x of 46.3 from a sample of size 26. (Give your answer correct to two decimal places.

While this campaign ended with a massive us military

While this campaign ended with a massive US military victory in which the Viet Cong were utterly destroyed as a fighting force, it is widely considered a major political defeat for the US because it initiated a major gro ...

The historical context of england in 1215 with the costs of

The historical context of England in 1215 with the costs of King Richard the Lionheart's ransom and the crusades. What were the nobles' complaints? How did the nobles' interests differ from the king's interest? What inte ...

Focusing on leadership and changeintroductionin this

Focusing on leadership and change Introduction In this assignment, we will focus on you, your relationship to leadership and change in your work context and the management ideas that have influenced those topics. Rather ...

1 one factor in determining the shelf life of a dry cereal

1) One factor in determining the shelf life of a dry cereal is the moisture content.  Since standard packaging techniques do not completely prevent cereal from absorbing moisture, the longer it stays on the shelf, the mo ...

1 in may the mean price of gas in the buffalo area was 2714

1. In May, the mean price of gas in the Buffalo area was $2.714 per gallon with a standard deviation of $0.045. In a sample of 32 gas stations, what percentage will have a price per gallon of gas between $2.695 and $2.72 ...

Please explain every step to make the sum understandableit

Please explain every step to make the sum understandable. It has been hypothesized that the distribution of seasonal colds in Canada is as follows: Season          Percentage Fall                    35% Winter            ...

How do you interpret the p-values in a regression output

How do you interpret the p-values in a regression output? What does a p-value of .0495 mean? What significance level is this?

Consumer reports provided extensive testing and ratings for

Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better per ...

  • 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