Question

A. Two independent samples have means of M₁ = 15 and M₂ = 12, with variances of s²₁ = 4 and s²₂ = 8. If the pooled variance is computed to be s²_p = 6, which of the following could be the sample sizes for each of the samples?

Group of answer choices

n1 = 30 and n2 = 5

n1 = 5 and n2 = 30

It CANNOT be any of these

n1 = 10 and n2 = 10

It could be ANY of these

B. A researcher conducts an independent samples study comparing two treatments and reports the t-stat as t(53) = 3.514. How many people in total participated in this study?

C. A researcher is comparing the amount of protein consumed by college athletes versus non-athletes, and has a sample of 20 athletes and 30 non-athletes. Which type of t-test is most appropriate?

Answer 1

Solution-A:

sp^2=(n1-1)*s1^2+(n2-1)*s2^2/n1+n2-2

By sustituiing n1 and n2 and verifying LHS=RHS
for n1=30 ,n2=5

LHS=sp^2=6

RHS=((30-1)*4+(5-1)*8)/(30+5-2)=4.484848

LHS not = RHS

case(ii)

n1=5,n2=30

LHS=sp^2=6

RHS=((5-1)*4+(30-1)*8)/(5+30-2)=7.515152

case(iii)

n1=10,n2=10

LHS=sp^2=6

RHS=((10-1)*4+(10-1)*8)/(10+10-2)=6

ANSWER(A)

n1=10 n2=10

Solution-B:

df=n1+n2-2

n1+n2=53+2

n1+n2=55

55 people in total participated in this study

ANSWER(B)

55

Solution-c::

C. A researcher is comparing the amount of protein consumed by college athletes versus non-athletes, and has a sample of 20 athletes and 30 non-athletes. Which type of t-test is most appropriate?

athletes and non athletes are 2 indpendent groups

and n1=n2<=30

perform independent sample t test

ANSWER(C)

independent samples t test