Independent random samples were selected from populations 1 and 2. The sample si

Question

Independent random samples were selected from populations 1 and 2. The sample sizes, means, and variances are as follows. Population 1 2 Sample Size 25 64 Sample Mean 11.4 7.4 Sample Variance 1.38 4.13 (a) Find a 95% confidence interval for estimating the difference in the population means (1 2). (Round your answers to two decimal places.) Independent random samples of size n1 = n2 = 100 were selected from each of two populations. The mean and standard deviations for the two samples were x1 = 125.8, x2 = 123.8, s1 = 5.5, and s2 = 6.4. (a) Construct a 99% confidence interval for estimating the difference in the two population means (1 2). (Round your answers to two decimal places.) to

Explanation / Answer

Sample 1 Size (n1): 25

Variance ( s12) = 1.38

Standard Deviation 1 (s1): 1.175

Sample 2 Size (n2): 64

Variance (s22) = 4.13

Therefore the 95% confidence interval for difference in the population mean is,

Pooled Variance
s2p = ((n1-1)*S1 + (n2-1)*S2) / (df1 + df2) = 5.51 / 87 = 0.06

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2))

= ((0.06/25) + (0.06/64))

= 0.06

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2)

= 4 ± (1.99 * 0.06)

= 4 ± 0.118

Result

1 - 2 = (M1 - M2) = 4, 95% CI [3.88, 4.12].

You can be 95% confident that the difference between your two population means (1 - 2) lies between 3.88 and 4.12

## x1 = 125.8, x2 = 123.8, s1 = 5.5, and s2 = 6.4 , n1=n2= 100

df1 +df2 = 100+100-2 = 198

Therefore the 99% confidence interval for difference between two mean is,

Pooled Variance
s2p = ((n1-1)*S1 + (n2-1)*S2) / (df1 + df2) = 71.21 / 198 = 0.36

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2))

= ((0.36/100) + (0.36/100))

= 0.08

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2)

= 2 ± (2.6 * 0.08)

= 2 ± 0.221

Result

1 - 2 = (M1 - M2) = 2, 99% CI [1.78, 2.22].

You can be 99% confident that the difference between your two population means (1 - 2) lies between 1.78 and 2.22

Sample 1 Mean (M1): 11.4

Sample 1 Size (n1): 25

Variance ( s12) = 1.38

Standard Deviation 1 (s1): 1.175

Sample 2 Mean (M2): 7.4

Sample 2 Size (n2): 64

Variance (s22) = 4.13

Standard Deviation 2 (s2): 2.033 df1 = n1-1 = 25-1 = 24 , df2 = n2-1 = 64-1= 63

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