You are conducting a study to see if the proportion of men over
50 who regularly have their prostate examined is significantly
different from 0.13. You use a significance level of
α=0.01α=0.01.
H0:p=0.13H0:p=0.13
H1:p≠0.13H1:p≠0.13
You obtain a sample of size n=289n=289 in which there are 45
successes.
1) What is p-value?
2) The p-value is...
3)This p-value leads to a decision to...
4) the final conclusion is that...
Part 1)
P = X / n = 45/289 = 0.1557
Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.1557 - 0.13 ) / ( √(( 0.13 * 0.87) /289))
Z = 1.30
P value = 2 * P ( Z > 1.2996 ) =
0.1937
Looking for the value Z = 1.30 in standard normal table to find the
P value.
Part 2)
Reject null hypothesis if P value < α = 0.01
Since P value = 0.1937 > 0.01, hence we fail to
reject the null hypothesis
Conclusion :- We Fail to Reject H0
greater than α
Part 3)
fail to reject the null
Part 4)
There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.13.
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