Given x 1 and x 2 distributions that are normal or approximately normal with unknown 1 and 2 , the value of t corresponding to x 1 x 2 has a distribution that is approximated by a Student's t distribution We use the convention that the degrees of freedom is approximately the smaller of n 1 1and n 2 1 However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula d f s 1 2 n 1 s 2 2 n 2 2 1 n 1 1 s 1 2 n 1 2 1 n 2 1 s 2 2 n 2 2 where s 1 , s 2 , n 1 , and n 2 are the respective sample standard deviations and sample sizes of independent random samples from the x 1 and x 2 distributions This is the approximation used by most statistical software When both n 1 and n 2 are 5 or larger, it is quite accurate The degrees of freedom computed from this formula are either truncated or not rounded (a) We tested whether the population average crime rate 2 in the Rocky Mountain region is higher than that in New England, 1 The data were n 1 15, x 1 3 51, s 1 0 91, n 2 13, x 2 3 87, and s 2 1 04 Use Satterthwaite's formula to compute the degrees of freedom for the Student's t distribution (Round your answer to two decimal places ) d f (b) Previously, you followed the convention that degrees of freedom d f smaller of n 1 1and n 2 1 Compare this value of d f with that found with Satterthwaite's formula The previous method leads to a d f that is always greater than or equal to that computed by Satterthwaite's formula The previous method leads to a d f that could be less than or greater than that computed by Satterthwaite's formula The previous method leads to a d f that is always equal to that computed by Satterthwaite's formula The previous method leads to a d f that is always less than or equal to that computed by Satterthwaite's formula

The Answer is in the image, click to view ...

Question: Given x 1 and x 2 distributions that are normal or approximately normal with unknown 1 and 2 , the value of t corresponding to

Givenx₁andx₂distributions that are normal or approximately normal with unknown₁and₂, the value oftcorresponding tox₁x₂has a distribution that is approximated by a Student'stdistribution. We use the convention that the degrees of freedom is approximately the smaller ofn₁1andn₂1.However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula:d.f.s₁²

n₁

+s₂²

n₂

n₁1

s₁²

n₁

2+1

n₂1

s₂²

n₂

wheres₁,s₂,n₁, andn₂are the respective sample standard deviations and sample sizes of independent random samples from thex₁andx₂distributions. This is the approximation used by most statistical software. When bothn₁andn₂are 5 or larger, it is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded.

(a) We tested whether the population average crime rate₂in the Rocky Mountain region is higher than that in New England,₁. The data weren₁=15,x₁3.51,s₁0.91,n₂=13,x₂3.87, ands₂1.04. Use Satterthwaite's formula to compute the degrees of freedom for the Student'stdistribution. (Round your answer to two decimal places.)

d.f.=

(b) Previously, you followed the convention that degrees of freedomd.f.=smallerofn₁1andn₂1.Compare this value ofd.f.with that found with Satterthwaite's formula.

The previous method leads to ad.f.that is always greater than or equal to that computed by Satterthwaite's formula.

The previous method leads to ad.f.that could be less than or greater than that computed by Satterthwaite's formula.

The previous method leads to ad.f.that is always equal to that computed by Satterthwaite's formula.

The previous method leads to ad.f.that is always less than or equal to that computed by Satterthwaite's formula.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Given x1 and x2 distributions that are normal or approximately normal with unknown Ï1 and Ï2, the value of t corresponding to 1 - 2 has a distribution that is approximated by a Students t...

help me in this problems A number of investigations have focused on the problem of assessing weights that can be lifted in a safe manner. A particular article proposed using a regression model to...

help me in this A number of investigations have focused on the problem of assessing weights that can be lifted in a safe manner. A particular article proposed using a regression model to relate the...

Question 1 (1 point) Determine the value of x after the following code is executed: x = 6 while x >= 2: X = X - 2 AY Determine the value of x after the following code is executed: X = 1 while x >= 2:...

Needs help with some SAS coding questions. 1. Try to find SAS macro samplhist() having two input parameters: dist and n. When run, your macro should sample n random variables from the specied...

PSY 230 Module 3 Assignment (A-3) For this assignment you will use multiple data sets, each embedded within the assignment below. Q1) Find the z values that form the boundaries of the critical region...

Expand Your Knowledge: Software Approximation for Degrees of Freedom Given x1 and x2 distributions that are normal or approximately normal with unknown s1 and s2, the value of t corresponding to x1...

Given x 1 and x 2 distributions that are normal or approximately normal with unknown 1 and 2 , the value of t corresponding to x 1 x 2 has a distribution that is approximated by a Students t...

Why will Disneyland never set its admission price at a level where its demand curve is inelastic? Use the total revenue and total cost curves to illustrate your answer.

Guthridge Soap Corporation is evaluating a new soap cutting machine that could eliminate some direct labor costs. The machine would cost $900,000 per year and would cost $0.10 per bar to cut the...

2. Proteins are natural polyamides which can be hydrolysed to form amino acids. The hydrolysis of proteins forms a mixture of colourless amino acids. Describe, with the aid of a labelled diagram, how...

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.