Calculate The Test Statistic And P-Value by ClassOf1

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Sub: Statistics                                                                     Topic: Hypothesis Testing

Calculate the Test Statistic and P-Value

Question:
Calculate the test statistic and p-value for each sample. Use Appendix below to calculate the p-value.




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 *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                              submitting the same in lieu of their academic submissions for grades.
Sub: Statistics                                                                     Topic: Hypothesis Testing




                                                                            Test Statistic             p-value

  H0: π = .30 versus H1: π ≠ .30, α = .05, x = 18, n = 40




Suppose you always reject the null hypothesis, regardless of any sample evidence.



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 *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                              submitting the same in lieu of their academic submissions for grades.
Sub: Statistics                                                                     Topic: Hypothesis Testing
What is the probability of Type I error?

 P(Type I error)




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 *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                              submitting the same in lieu of their academic submissions for grades.
Sub: Statistics                                                                        Topic: Hypothesis Testing

Solution:
H0: π = .30 versus H1: π ≠ .30, α = .05, x = 18, n = 40

The information in the given problem can be represented with the following notations:

Null Hypothesis: H0: P = 0.30

That is, the population proportion is equal to 0.30

Alternate Hypothesis: H1: P ≠ 0.30

That is, the population proportion is not equal to 0.30

Test Statistic:

The test statistic is:

         p P
Z
          P *Q
            n

Thus, P = 0.30

       Q = 1 – P = 1 – 0.30 = 0.70

p = X/n = 18/40 = 0.45

Therefore,

        0.45 0.30
Z
         0.30 * 0.70
             40


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    *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                                 submitting the same in lieu of their academic submissions for grades.
Sub: Statistics                                                                      Topic: Hypothesis Testing
       0.15
 =
      0.00525

= 2.0702 ~ 2.07

Thus, the test statistic is 2.07


The p-value of the test statistic is calculated as follows:

P (Z > z) = 2 * (1 – P (Z < z)) = 2 * (1 – 0.9808) (by referring the Appendix C – 2)

                            = 0.0384

Therefore, the required p-value is 0.0384

Hypothesis                                                                                  Test statistic   
								
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