Question

1. Consider sample data with

• = 20 and
• s = 4.

(For each answer, enter an exact number.)

(b) Compute a 75% Chebyshev interval around the sample mean.
Lower Limit =
Upper Limit =

2. How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x	3	6	12	14	22
y	60	95	140	170	179

(a)

Make a scatter diagram of the data and visualize the line you think best fits the data. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

(b)

Would you say the correlation is low, moderate, or strong?

lowmoderate    strong

Would you say the correlation is positive or negative?

positive or negative    

(c)

Use a calculator to verify that Σ(x) = 57, Σ(x²) = 869, Σ(y) = 644, Σ(y²) = 93,166, and Σ(x y) = 8,748.

Compute r. (Enter a number. Round your answer to three decimal places.)


As x increases from 3 to 22 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to remain constant as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.    Given our value of r, y should tend to increase as x increases.Given our value of r, y should tend to decrease as x increases.

Answer 1

(b) Compute a 75% Chebyshev interval around the sample mean.

According to Chebyshev 1-1/k^2=1-1/2^2=0.75 l=75% of the data lie within k standard deviation(k=2) of the mean
Lower Limit =mean-k*sigma=20-2*4=12
Upper Limit =mean+k*sigma=20+2*4=28

Rcode to get scatterlot

x <- c(3,   6   ,12,   14,   22)
y <- c(60   ,95,   140   ,170,   179)  
plot(y~x,pch=16)

Output:

From scatterplot we observe

strong positive relationship exists between x and y

ANSWER(B)

strong

positive

ANSWER(C)

x <- c(3,   6   ,12,   14,   22)
y <- c(60   ,95,   140   ,170,   179)  
cor.test(x,y)

cor.test function in R to get r value

data: x and y
t = 4.759, df = 3, p-value = 0.01761
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.3359883 0.9961185
sample estimates:
cor
0.9396987

ANSWER(c)

r=0.940

as x increases ,y increases as relationship is positive

Given our value of r, y should tend to increase as x increase