Question

use r-studio code to compute

1. Let T ∼ t – distributed with the given degrees of freedom (df),
then compute the following probabilities with a nice little picture
beside each problem: [5 points]

(e) df = ∞, P(T > 2.3)

2. Let T ∼ t – distributed with the given degrees of freedom
(df), compute the following quantiles (percentiles) with a nice
little picture beside each problem: [5 points]

(a) df = 2, 0.05th percentile

(b) df = 7, 7th percentile

(c) df = 50, 0.2nd percentile

(d) df = 27, 0th percentile

(e) df = ∞, 97.5th percentile

3. For given ¯x, µ, s, and n, compute the following probabilities
for the random variable

T =

¯ x−µ s/√n, where T ∼ t – distributed with n−1 degrees of freedom. [8 points]

(a) n = 29, µ = 5, ¯ x = 4.5, s = 1.05. Compute P(T < t).

(b) n = 10, µ = 50, ¯ x = 45, s = 7.25. Compute P(T > t).

(c) n = 11, µ = 19, ¯ x = 20, s = 2.32. Compute P(|T| < t).

(d) n = 20, µ = 25, ¯ x = 26.28, s = 7.5. Compute P(|T| > t).

Answer #1

R codes :

#QUESTION : 3

> T_stat=function(n,mu,x,s)

+ {

+ T=sqrt(n)*(x-mu)/s

+ return(T)

+ }

#(a) P(T<t)

> pt(T_stat(29,5,4.5,1.05),29-1,lower.tail=T)

[1] 0.007994645

#(b)P(T>t)

> pt(T_stat(10,50,45,7.25),10-1,lower.tail=F)

[1] 0.9714538

#(c) P(|T|<t) = P(T<t)-P(T<-t)

>
pt(T_stat(11,19,20,2.32),11-1,lower.tail=T)-pt(-(T_stat(11,19,20,2.32)),11-1,lower.tail=T)

[1] 0.8166736

#(d) P(|T|>t) = P(T>t)+P(T<-t)

>
pt(T_stat(20,25,26.28,7.5),20-1,lower.tail=F)+pt(-(T_stat(20,25,26.28,7.5)),20-1,lower.tail=T)

[1] 0.4546908

Let f : R \ {1} → R be given by f(x) = 1 1 − x . (a) Prove by
induction that f (n) (x) = n! (1 − x) n for all n ∈ N. Note: f (n)
(x) denotes the n th derivative of f. You may use the usual
differentiation rules without further proof. (b) Compute the Taylor
series of f about x = 0. (You must provide justification by
relating this specific Taylor series to...

1.
lm(EARNINGS~S+EXP) (in R),
the underlying assumption was that EARNINGS is a normally
distributed random variable with an expected value given by a
constant, but unknown value (represented by the Greek letter "mu")
that we are trying to estimate.
True or False?
2.
In our typical simulation program, when we save some number like
1,000 or 10,000 replications for some statistic like a t-ratio or
an F-statistic, the purpose of a summary command such as
mean(abs(ts) > qt(.975,df) ) or...

X Y 1 50 8 57 11 43 16 18 20 18 Use the estimated regression
equation is y = 61.5 – 2.21x. A). Compute the Mean Square Error
Using Equation. S^2 = MSE = SSE/(n-2) B). Compute The Standard
Error of the estimate using equation. S = SQRT(MSE) =
SQRT[SSE/(n-2)] C). Compute the estimated Standard Deviation of b1
using equation. Sb1 = S/SQRT[SUM(x-(x-bar))^2] D). Use the t-test
to test the following hypothesis (α = 0.05) H0: β1 = 0...

9.3 Hmwk - Confidence Interval for Population Mean
(Homework)
Given a variable that has a t distribution with the specified
degrees of freedom, what percentage of the time will its value fall
in the indicated region? (Round your answers to one decimal
place.)
(a) 10 df, between -1.37 and 1.37
%
(b) 10 df, between -2.76 and 2.76
%
(c) 24 df, between -2.06 and 2.06
%
(d) 24 df, between -2.80 and 2.80
%
(e) 23 df, outside the...

1. The breaking strengths (measured in dynes) of nylon fibers
are normally distributed with a
mean of 12,500 and a variance of 202,500.
a) What is the probability that a fiber strength is more than
13,175?
b) What is the probability that a fiber strength is less than
11,600?
c) What is the probability that a fiber strength is between 12,284
and 15,200?
d) What is the 90 th percentile of the fiber breaking strength?
2.
Suppose that X, Y...

ACT Prep Course. ACT prep courses like to market that you can
increase your ACT score by taking their courses. Some statisticians
were curious how effective these courses really were. They decided
to investigate the truth of the claim by measuring the average
score increase for a random sample of students selected to take an
ACT prep course. These students took the ACT twice, once before and
once after taking the course. The variable of interest was the
increase in...

Given are five observations for two variables, x and y .
xi
1
2
3
4
5
yi
53
58
47
21
11
Use the estimated regression equation is y-hat = 78.01 -
3.08x
A.) Compute the mean square error using
equation.
s^2 = MSE = SSE / n -2
[ ] (to 2 decimals)
B.) Compute the standard error of the estimate
using equation
s = sqrtMSE = sqrt SSE / n - 2
[ ] (to 2 decimals)...

Use a t-test to test the claim about the population mean μ at
the given level of significance α using the given sample
statistics. Assume the population is normally distributed.
Claim: μ ≠ 24; α=0.10 Sample statistics: x overbar =
21.4, s = 4.2 , n equals = 11
What are the null and alternative hypotheses? Choose the
correct answer below.
A.H0: μ≠24
Ha: μ=24
B.H0: μ≤24
Ha: μ>24
C.H0: μ=24
Ha: μ≠24
D.H0: μ≥24
Ha: μ than<24...

*Answer all questions using R-Script*
Question 1
Using the built in CO2 data frame, which contains data from an
experiment on the cold tolerance of Echinochloa crus-galli; find
the following.
a) Assign the uptake column in the
dataframe to an object called "x"
b) Calculate the range of x
c) Calculate the 28th percentile of
x
d) Calculate the sample median of
x
e) Calculate the sample mean of x and
assign it to an object called "xbar"
f) Calculate...

1. Let x be a continuous random variable. What is the
probability that x assumes a single value, such as a (use numerical
value)?
2. The following are the three main characteristics of a normal
distribution.
The total area under a normal curve equals _____.
A normal curve is ___________ about the mean. Consequently, 50%
of the total area under a normal distribution curve lies on the
left side of the mean, and 50% lies on the right side of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 21 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago