Sample 1 has n1 independent random variables (X1, X2, ...Xn1) following normal distribution, N(µ1, σ21); and...

Sample 1 has n₁ independent random variables (X₁, X₂, ...X_n1) following normal distribution, N(µ1, σ²₁); and Sample 2 has n₂ independent random variables (Y₁, Y₂, ...Y_n2 ) following normal distribution, N(µ2, σ²₂). Suppose sample 1 mean is X bar, sample 2 mean is Y bar , and we know n₁ ,n₂ , σ²₁ and σ²₂. Construct a Z statistic (i.e. Z~N(0, 1)) to test H0 : µ₁ = µ_2.

Solutions

Expert Solution

Assumed values,
mean(x)=5279
standard deviation , sigma1 =148
number(n1)=410
y(mean)=5248
standard deviation, sigma2 =208
number(n2)=410
null, Ho: u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=5279-5248/sqrt((21904/410)+(43264/410))
zo =2.46
| zo | =2.46
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo | =2.459 & | z alpha | =1.96
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.46 ) = 0.01394
hence value of p0.05 > 0.01394,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: μ1 != u2
test statistic: 2.46
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.01394
we have enough evidence to support the claim that difference between two independent samples.

orchestra answered 1 year ago

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