Assume that you have a sample of n1-7, with the sample mean X1 50, and a sample
ID: 3158486 • Letter: A
Question
Assume that you have a sample of n1-7, with the sample mean X1 50, and a sample standard deviation of S1 5, and you have an independent sample of n2 17 from another population with a sample mean of X2-34, and the sample standard deviation S2-6. Construct a 99% confidence interval estimate of the population mean difference between 1 and 2. Click here for page 1 of critical values of t Click here for page 2 of critical values of t 34, and the sample standard deviation S2-6. Construct a (Type an integer or decimal rounded to two decimal places as needed.)Explanation / Answer
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)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=50
Standard deviation( sd1 )=5
Sample Size(n1)=7
Mean(x2)=34
Standard deviation( sd2 )=6
Sample Size(n2)=17
CI = [ ( 50-34) ±t a/2 * Sqrt( 25/7+36/17)]
= [ (16) ± t a/2 * Sqrt( 5.69) ]
= [ (16) ± 3.707 * Sqrt( 5.69) ]
= [7.16 , 24.84]