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Samples from two independent, normally-distributed populations produced the following results.

Population 1 Population 2
Sample size 7 9
Sample mean 15.9 12.6
Sample standard deviation 10.2 13.4

Calculate the 95% confidence interval for the difference between population means μ1-μ2

a. 1.889
b. 8.6
c. 1.128
d. 1.286

User Cyberlobe
by
7.2k points

1 Answer

6 votes

Answer: The 95% confidence interval for the difference between population means μ1-μ2 is
(-9.36,\ 15.96) .

Explanation:

Given : Samples from two independent, normally-distributed populations produced the following results.

Population 1 Population 2

Sample size 7 9

Sample mean 15.9 12.6

Sample standard deviation 10.2 13.4

The confidence interval for the difference between population means μ1-μ2 is given by :-


\overline{X_1}-\overline{X_2}\pm t^*\sqrt{(s_1^2)/(n_1)+(s_2^2)/(n_2)}

, where
n_1 = sample size from population 1


n_1 = sample size from population 2


\overline{X_1}-\overline{X_2} = Difference between sample mean of two population


s_1= Sample standard deviation of population 1.


s_2= Sample standard deviation of population 2.

t* = Critical value for
df=n_1+n_2-2 and significance
\alpha/2.

As per given :


n_1=7
n_2=9

df = 7+9-2=14


\overline{X_1}-\overline{X_2}=15.9-12.6=3.3


s_1=10.2
s_2=13.4


\alpha=1-0.95=0.05

Critical t-value :
t_(df, \alpha/2)=t_(14, 0.025)=2.145

So , the 95% confidence interval for the difference between population means μ1-μ2 would be


3.3\pm (2.145)\sqrt{(10.2^2)/(7)+(13.4^2)/(9)}


3.3\pm (2.145)√(14.86+19.95)


3.3\pm (2.145)√(34.81)


3.3\pm (2.145)(5.9)


3.3\pm 12.66


(3.3-12.66,\ 3.3+12.66)=(-9.36,\ 15.96)

Hence, the 95% confidence interval for the difference between population means μ1-μ2 :
(-9.36,\ 15.96)

User Fatos
by
6.8k points
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