Consider two independent populations that are normally distributions. A simple random sample of n_1=41 from the first population showed bar x_11=33, a

Kaycee Roche

Kaycee Roche

Answered question

2021-03-11

Consider two independent populations that are normally distributions. A simple random sample of n1=41 from the first population showed x11=33, and a simple random of size n2=48 from the second population showed
x2=32
Suppose s1=9s1=9ands2=10s2=10, find a 98% confidence interval for μ1μ2μ1μ2. (Round answers to two decimal places.)
margin of error-?
lower limit-?
upper limit-?

Answer & Explanation

dieseisB

dieseisB

Skilled2021-03-12Added 85 answers

Step 1
From the provided information,
n1=41
x1=33
n2=48
x2=32
s1=9
s2=10
The confidence level =98%
Level of significance (α)=10.98=0.02
The degree of freedom =n1+n22=41+482=87
The critical value of t at 87 degree of freedom with 0.02 level of significance from the t value table is 2.37.
Step 2
The pooled standard deviation can be obtained as:
sp=(n11)s12+(n21)s22n1+n22
=(411)(9)2+(481)(10)241+482
=9.553
The required margin of error can be obtained as:
E=t(sp1n1+1n2)
=(2.37)(9.553141+148)
4.81
Thus, the margin of error is 4.81.
Step 3
The required 98% confidence interval for μ1μ2 can be obtained as:
CI=(x1x1)±E
=(3332)±4.81
=1±4.81
=(3.81,5.81)
Thus, the lower limit of confidence interval is -3.81 and the upper limit is 5.81.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-11Added 2605 answers

Answer is given below (on video)

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