Question

Give a 98% confidence interval, for μ1−μ2μ1-μ2 given the following information.

n1=35n1=35, ¯x1=2.69x¯1=2.69, s1=0.7s1=0.7
n2=40n2=40, ¯x2=3.15x¯2=3.15, s2=0.46s2=0.46

±±   Rounded to 2 decimal places

Answer 1

solution:

Given data

1 = 2.69 , S1 = 0.7 , n1 = 35

   2 = 3.15 , S2 = 0.46 , n2 = 40

For 98% confidence level , = 1 - CL = 1 - 0.98 = 0.02

Z(/2) = Z(0.01) = 2.33 [using Z distribution table ]

The confidennce interval for difference between two means is given by

CI : (1 - 2 ) ± Z *

: (2.69 - 3.15)  ± 2.33 *

: -0.46  ± 0.324

: ( -0.784 , -0.136)

Therefore , 98% confidence interval is -0.78 < < -0.14

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