Question

9) In a sample of 400 people selected randomly from one town, it is found that 130 of them are Gamecock Fans. At the 0.05 significance level, test the claim that the proportion of all people in the town who are Gamecock fans is 27%.

A] What type of statistical test can be used here?

a. Z-test of proportions            c. F Test                                e. Either c² or λ Test

b. a-Test of proportions           d. Either T or F-Test               f. T-Test

          

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B] What is the stated claim about the proportion?

a. p = 0.27 The population proportion is the same as 27%.

b. p ≠ 0.27 The population proportion is different from 27%.

c. p > 0.27 The population proportion is greater than 27%.

d. p < 0.27 The population proportion is less than 27%.

e. p ≥ 0.27 The population proportion is greater than or equal to 27%.

f. p ≤ 0.27 The population proportion is less than or equal to 27%.

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C] What are the null hypothesis (H₀) and the alternative hypothesis (H_a)? Circle one answer out of the “a” through “f” choices below.

                                    a. H₀: p > 0.27                           d. H_a: p < 0.27  

H_a:p ≤ 0.27                                     H₀: p ≥ 0.27

b. H₀: p = 0.27                           e. H_a: p = 0.27  

H_a: p ≠ 0.27                                   H₀: p ≠ 0.27

c. H_a: p > 0.27                            f. H₀: p < 0.27  

H₀: p ≤ 0.27                    H_a: p ≥ 0.27

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D] Is this test:       a. Fat tailed?                          d. Inverse tailed?

b. Two tailed?                        e. Left tailed?

c. Right tailed?                       f. Meta-tailed?

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E] What is the numerical value of the test statistic (TS) calculated from the observed data?

a. 0.5558          b. 2.4777     c. 1.9600     d. 2.0917     e. 0.6456     f. 0.6234

      

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F] Provide EITHER the Critical Value (CV) OR the p-value

Critical Value (CV):

a. z = 2.05       b. z = 1.643 c. z = 1.96 d. z = 1.645         e. z = 2.576           f. z = 2.03

     

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P-value:

a. 0.4210         b. 0.6830     c. 0.0132   d. 0.5321            e. 0.6283              f. 0.5221

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G] For this problem about Gamecock fans, what is your decision about H₀ (the null hypothesis)?

a. Fail to reject the claim         c. Fail to reject H₀                   e. Accept H₀        

b. Reject H₀                           d. Reject the claim         f. Accept the claim

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(9 continued)

H] For this problem about Gamecock fans, what is the decision about the original claim?

a. At the 5% level, there is NOT enough evidence to reject the claim that the proportion is 27%.

b. At the 10% level, there is enough evidence to reject the claim that the proportion is 27%.

c. At the 5% level, there is enough evidence to reject the claim that the proportion is 27%.

d. At the 10% level, there is NOT enough evidence to reject the claim that the proportion is 27%.

e. At the 5% level, there is enough evidence to support the claim that the proportion is 27%.

f. At the 10% level, there is enough evidence to support the claim that the proportion is 27%.

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Answer 1

Answers:

A. Z-Test of Proportions

B. p = 0.27 The population proportion is the same as 27%.

C. Ho: p = 0.27 vs Ha: p ≠ 0.27

D. Two-Tailed Test

E. 2.4777

F. z = 1.96 and  p-value = 0.0132

G. Reject Ho

H. At the 5% level, there is enough evidence to reject the claim that the proportion is 27%.