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

A] What type of statistical test can be usedhere?

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

b. a-Test ofproportions          d. Either T orF-Test              f. T-Test

          

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B] What is the stated claim about theproportion?

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

b. p ≠ 0.27 The population proportionis different from 27%.

c. p > 0.27 The populationproportion is greater than 27%.

d. p < 0.27 The populationproportion is less than 27%.

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

f. p ≤ 0.27 The population proportionis 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  _{                      Â} d. H_a: p < 0.27  

H_a:p ≤0.27_{                              Â} Â Â Â Â  H₀: p ≥ 0.27

b. H₀: p =0.27  _{                      Â} e. H_a: p = 0.27  

H_a: p ≠0.27_{                            Â} Â Â Â Â  H₀: p ≠ 0.27

c. H_a: p >0.27  _{                       Â} f. H₀: p < 0.27  

H₀: p ≤0.27                   H_a: p ≥ 0.27

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

b. Twotailed?                       e. Left tailed?

c. Righttailed?                      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 = 1.96d. 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 yourdecision about H₀ (the nullhypothesis)?

a. Fail to reject theclaim         c. Fail torejectH_{0                 Â} e. Accept H₀       

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

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H] For this problem about Gamecock fans, what is thedecision about the originalclaim?

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

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

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

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

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

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

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