Stat 230编程语言代做、R编程设计调试

日期：2021-04-11 10:34

Stat 230 Assignment 6 2020W2

Question 1

Suppose we have I samples (each of size J): X1, X2, · · · , XI , taken from each of I possibly

different populations. All observations are independent, inside and between the samples. The

table below shows information of each samples

Sample

Observation in

Each Sample

Question 2

(8 points)An experiment was conducted in which four brands of tires were compared for traction

on ice. Three measurements of stopping distance were taken for each type of tire.

In the experiment, a single car was used. In each experimental run, the distance over which

the car could decelerate from 20 km/h to 0 km/h on an artificial ice surface was measured.

Tire Brand Stopping Distance

Compute the treatment group averages and the residuals. Do the ANOVA and decide whether

the true mean stopping distances are different for the different brands at the .05 level.

Question 3

(5 points) The time in months before paint started to peel for five brands of paint applied to

a set of test panels is summarized below:

Paint No. of Panels ˉxi· s

2

A 6 48.6 30.5

B 6 51.2 30.2

C 6 60.1 31.8

D 6 55.2 33.1

On the basis of residual plots, the data can be modeled as normal, and the measurements

appear to be independent. Is there evidence at the 5% level of a difference in the mean time

to peel for the different panels?

Question 4

(4 points)The data set PlantGrowth is available in R. It contains weight measurements on

30 plants grown under 3 different experimental conditions (10 in each condition). Here is the

output from the aov command in R:

Df Sum Sq Mean Sq F value Pr(>F)

group 2 3.7663 1.8832 4.8461 0.01591 *

Residuals 27 10.4921 0.3886

Is there evidence that at least one experimental condition yields plants of a different mean

weight?

Question 5

An individual’s critical flicker frequency (cff) is the highest frequency (in cps) at which the

flicker in a flickering light source can still be detected. At frequencies above the cff, the light

source appears to be continuous even though it is actually flickering. A preliminary investigation

was conducted to see if true average cff depends on iris color. The results are given below from

an ANOVA carried out in R. An equal number of rats were fed one of three diets (Beef, Pork,

or Cereal) in order to investigate weight gain. The partial results from an ANOVA carried out

in R follow below.(Data sourced from the graonva package in R)

Df Sum Sq Mean Sq F value

Diet 267

Residuals 57 15932

(a) (1 point) How many rats were used in this study?

(b) (4 points) Complete this ANOVA table and interpret the result of the associated F-test.

Question 6

(8 points) Suppose x1, x2, . . . , xn come from a Poisson distribution p(x) = e?λλ

x

x!

, where x =

0, 1, 2, . . . with unknown parameter λ. Find the maximum likelihood estimator for λ.

Question 7

(5 points) Consider a population governed by the discrete distribution p(x), where p(x) = θ

for x = 1 and p(x) = 1 ? θ for x = 0, where θ ∈ [0, 1]. Three independent observations are

{0, 1, 0}. Find the likelihood function

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Question 8

Suppose 5 independent measurements 1, 3, 1, 7, 3 are taken from an exponentially distributed

population f(x) = λe?λx

, where x > 0

(a) (5 points) Find the maximum likelihood estimate for λ.

(b) (4 points) Find the maximum likelihood estimate for the probability that the next independent

measurement taken from the population is greater than 3.

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