Question

You are conducting a study to see if the proportion of men over 50 who regularly...

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...

  • less than (or equal to) αα
  • greater than α

3)This p-value leads to a decision to...

  • reject the null
  • accept the null
  • fail to reject the null

4) the final conclusion is that...

  • 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.
  • There is not 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.
  • The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.13.
  • There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.13.

Homework Answers

Answer #1

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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