The average annual cost to attend for a sample of 10 private colleges was $42,50

Question

The average annual cost to attend for a sample of 10 private colleges was $42,500, with a standard deviation of $6,980 while for a sample of 12 public colleges the sample average was $22,300 with a sample standard deviation of $4,530.

a. What is the estimate of the difference between the population mean annual cost of attendance between private and public colleges based on these two samples?

b. Assuming equal population variances, what is the 99% confidence interval for the difference in the population mean annual costs of attendance for private and public colleges?

Explanation / Answer

a.
estimate of the difference between the population mean between private and public = ( 42500-22300) = 20200
b.
CI = x1 - x2 ± t a/2 * Sqrt(S^2(1/n1+1/n2))
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=42500
Standard deviation( sd1 )=6980
Sample Size(n1)=10
Mean(x2)=22300
Standard deviation( sd2 )=4530
Sample Size(n2)=12
S^2 = (9*48720400 + 11*20520900) / (22- 2 )
S^2 = 33210675
CI = [ ( 42500-22300) ± t a/2 * 5762.87 Sqrt( 1/10+1/12)]
= [ (20200) ± t a/2 * 5762.87 * Sqrt( 0.183) ]
= [ (20200) ± 2.001 * 5762.87 * Sqrt( 0.183) ]
= [ (15262.505 , 25137.495 ]

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