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

A psychologist measures units of change for a memory test

A psychologist measures units of change for a memory test after students are given an opportunity to sleep only four hours. The following change units were obtained: 7, -12, 4, -7, 3, -10. Find the a) mean, b) median, c) ...

Describe the collapse of the soviet union begin with the

Describe the collapse of the Soviet Union. Begin with the events during the 1980s including the entire Gorbachev era. Should include at least the following topics: 1. Poland's democratic revolution of the 1980s 2. Gorbac ...

Find the indicated area under the standard normal curve to

Find the indicated area under the standard normal curve. To the left of z= - 1.96 The area to the left of z = -1.96 under the standard normal curve is __.(Round to four decimal places as needed.)

A repeated-measures experiment comparing only two

A repeated-measures experiment comparing only two treatments can be evaluated with either a t statistic or an ANOVA. As we found with the independent-measures design, the t test and the ANOVA produce equivalent conclusio ...

At a university the average cost of books per student has

At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sampl ...

1 whats so bad about making a type i error2 how does the

1. What's so bad about making a Type I error? 2. How does the Bonferroni adjustment control for Type I error when many statistical tests are conducted? 3. Why do researchers use ANOVA rather than t-tests to analyze data ...

Data show that narcissistic people who have a grandiose

Data show that narcissistic people (who have a grandiose, inflated perception of themselves) often fly into a "narcissistic rage" when things don't go their way. (In other words, they throw a temper tantrum.) A resea ...

1 use your own random mu sigma to generate four sets of

1) Use your own random (μ, σ) to generate four sets of (normal-distribution based) random numbers (i.e., samples) of sizes n = 5, 20, 80, and 320, respectively. 2) Calculate the means and standard deviations for the 4 sa ...

An auditor claims that the average annual salary of a

An auditor claims that the average annual salary of a project manager at a construction company exceeds $82,000. A random sample of 20 project managers had an average salary of $89,600 with a sample standard deviation of ...

The distribution of starting salaries of men who received

The distribution of starting salaries of men who received college degrees last year had a mean equal to 31000 and a standard deviation equal to 1200. A random sample of 36 starting salaries of women who received college ...

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen