Question

The proportion of adults who wear costumes to work on St. Patrick’s Day is claimed to be greater than 0.12. 20 working adults are randomly selected from across the nation and 2 of them wore costumes to work on St. Patrick’s Day. Use ? = 0.05. Choose closest answer wherever necessary.

1.) Identify the definition of this test.

A. H0 : p > 0.12 H1 : p < 0.12

B. H0 : p ? 0.12 H1 : p > 0.88

C. H0 : p < 0.12 H1 : p > 0.88

D. H0 : p ? 0.12 H1 : p < 0.88

E. H0 : p ? 0.12 H1 : p > 0.12

2.) What is the test statistic (closest answer)?

A. -0.45

B. -2.12

C. 1.33

D. -0.3

E. 0.05

3.) What is the critical value for this test?

A. 2.44

B. 2.13

C. 1.64

D. 2.38

E. 2.18

4.)What is the p-value for this test?

A. 0.6172

B. 0.792

C. 0.2652

D. 0.183

E. 0.3443

5.)Identify the true statement about this test.

A. At a 95% confidence level we do not reject H1 as there is 38.28% probabilistic support toward the null hypothesis.

B. At a 5% confidence level we do not reject H0 as there is 38.28% probabilistic support toward the alternative hypothesis.

C. At a 95% confidence level we do not reject H0 as there is 38.28% probabilistic support toward the null hypothesis.

D. At a 95% confidence level we do not reject H0 as there is 38.28% probabilistic support toward the alternative hypothesis.

E. At a 5% confidence level we do not reject H0 as there is 61.72% probabilistic support toward the alternative hypothesis.

Answer 1

n = 20

? = 0.05

p > 0.12

So, the hypothesis will be -

1)

H0 : p ? 0.12

H1 : p > 0.12

Because we need to verify the claim if p is greater than 0.12 and so because there is a > it cannot come in the Null Hypothesis

That will be option (E)

2)

? = sqrt[ P * ( 1 - P ) / n ] = sqrt(0.12*0.88/20) = 0.073

p1 = 2/20 = 0.1

Test statistic, Z = (p1-p)/? = (0.1-0.12)/0.073 = -0.274

That will be option (D)

3) Critical value= Z at 95% CI for one-sided test = 1.65

That will be option (C)

4) p-value:P(Z<-0.274) + P(Z>-0.274) = 2*0.3916 = 0.792

So, that will be (B)

5) p>?  

So, at 95% confidence, we do not reject H0 as there is 38.28% probabilistic support toward the null hypothesis

So, that will be option (C)

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