11. Assume that you plan to use a significance level of α = 0.05
to test the claim that Pl = P2· Use the given sample sizes and
numbers of successes to find the P-value for the hypothesis
test.
n1=60, n2=75, x1=20, x2=35
Given Data
For sample 1
sample size is N1 = 60
Number of favorable cases is X1=20
sample proportion is
For sample 1
sample size is N2 = 75
Number of favorable cases is X2=35
sample proportion is
pooled proportion is computed as
Since we plan to use a significance level of α = 0.05 to test the claim that Pl = P2.Null and alternative hypotheses need to be tested is
Ho : p1 = p2 (claim)
Ha : p1 ≠ p2
This corresponds to a two-tailed test
The significance level is α=0.05, and the critical value for a two-tailed test is
zc (lower)= -1.96 using excel formula =NORM.S.INV(0.025)
zc (upper)= 1.96 using excel formula =NORM.S.INV(0.975)
The rejection region for this two-tailed test is
R = z < -1.96 & z > 1.96
Test statistics
Since z = - 1.567 and fall in non rejection region, null hypothesis is not rejected.
The p-value is p = 0.1172 using excel formula =2*NORM.S.DIST(-1.567,TRUE)
and since p = 0.1172 > 0.05, It is concluded that the null hypothesis is not rejected.
Answer is p value = 0.1172
11. Assume that you plan to use a significance level of α = 0.05 to test...
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