independent random sample of size n1=16 and n2= 25 from a normal population with standard deviation1=4.8...

independent random sample of size n1=16 and n2= 25 from a normal population with standard deviation1=4.8 and standard deviation 2=3.5 have the mean x bar1=18.2 and xbar2=23.4 find the 90% confidence interval for mew1-mew 2

Expert Solution

Given,

1 = 18.2, 2 = 23.4 , S1 = 4.8 , S2 = 3.5, n1 = 16, n2 = 25

Pooled standard deviation Sp= Sqrt ( [ (n1-1) S²1 + (n2 - 1)S²2 ] / n1 + n2 - 2 )

= Sqrt( 15 * 4.8² + 24 * 3.5² / (16 + 25 - 2) )

= 4.0497

df = n1 + n2 - 2 = 16 + 25 - 2 = 39

t critical value at 0.10 siginficance level for 39 df = 1.685

90% confidence interval for 1 - 2 is

(1 - 2) - t * Sp * sqrt(1/n1 + 1/n2) < 1 - 2 < (1 - 2) + t * Sp * sqrt(1/n1 + 1/n2)

(18.2-23.4) - 1.685*4.0497*sqrt(1/16+1/25) < 1-2 < (18.2 - 23.4) + 1.685*4.0497*sqrt(1/16+1/25)

-5.2 - 2.1847 < 1 - 2 < -5.2 + 2.1847

-7.3847 < 1 - 2 < -3.0153

Confidence interval for 1 - 2 is (-7.3847 , -3.0153 )

milcah answered 2 months ago

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