The following results are for independent random samples taken from two populati
ID: 3125358 • Letter: T
Question
The following results are for independent random samples taken from two populations.
Sample 1 Sample 2
n1 = 20 n2 = 30
x¯1 = 22.5 x¯2 = 20.1
s1 = 2.5 s2 = 4.8
What is the point estimate of the difference between the two population means? (to 1 decimal)
b. What is the degrees of freedom for the t distribution? (to 1 decimal)
c. At 95% confidence, what is the margin of error? (to 1 decimal)
d. What is the 95% confidence interval for the difference between the two population means? (to 1 decimal)
Explanation / Answer
a. point estimate of the difference = x1 - x2 = ( 22.5-20.1) = 2.4
b.
with Min (n1-1, n2-1) i.e 19 d.f
c.
M.E = t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=22.5
Standard deviation( sd1 )=2.5
Sample Size(n1)=20
Mean(x2)=20.1
Standard deviation( sd2 )=4.8
Sample Size(n1)=30
M.E = t a/2 * Sqrt( 6.25/20+23.04/30)
= 2.093 * Sqrt( 1.0805)
= 2.1756
d.
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
CI = [ ( 22.5-20.1) ±t a/2 * Sqrt( 6.25/20+23.04/30)]
= [ (2.4) ± t a/2 * Sqrt( 1.0805) ]
= [ (2.4) ± 2.093 * Sqrt( 1.0805) ]
= [0.2244 , 4.5756]