Consider the following data for two independent random samples taken from two no

Question

Consider the following data for two independent random samples taken from two normal populations. Sample 1 10 7 13 7 9 8 Sample 2 8 7 8 4 6 9 a. Compute the two sample means Sample 1: Answer Sample 2: Answer b. Compute the two sample standard deviations (to 2 decimals). Sample 1: Answer Sample 2: Answer c. What is the point estimate of the difference between the two population means? Answer d. What is the 90% confidence estimate of the difference between the two population means (to 2 decimals)? ( Answer, Answer )

Explanation / Answer

a)

sample mean of sample1(xbar1 )= 9

sample mean of sample 2 (xbar1)= 7

b)

standarddevaition of sample1 = 2.28

standarddevaition of sample2= 1.79

c)

Point estimate = xbar1-xbar2 = 9-7 = 2

d)

a=

alpha = a-CI = 1-0.90 = 0.1

a/2 = 0.05

df = 9

from students t table

t(a/2,df) = t(.05,9) = 1.8331

CI of  the difference between the two population means =

(xbar1-xbar2) +/- t*sqrt(s1^2/n1+s2^2/n2)

so,

CI =( (9-7)-1.8331*sqrt(2.28^2/6+1.79^2/6) to (9-7)+1.8331*sqrt(2.28^2/6+1.79^2/6) )

= ( -0.17 to 4.17)

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