Construct a 90% interval estimate of the ratio of the population variances using
ID: 3130622 • Letter: C
Question
Construct a 90% interval estimate of the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. Use Table 4. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Construct a 90% interval estimate of the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. Use Table 4. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
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)=159
Standard deviation( sd1 )=4.99
Sample Size(n1)=7
Mean(x2)=156.9
Standard deviation( sd2 )=4.517
Sample Size(n2)=6
CI = [ ( 159-156.9) ±t a/2 * Sqrt( 24.9001/7+20.403289/6)]
= [ (2.1) ± t a/2 * Sqrt( 6.96) ]
= [ (2.1) ± 2.015 * Sqrt( 6.96) ]
= [-3.22 , 7.42]