In order to conduct a hypothesis test for the population proportion, you sample

Question

In order to conduct a hypothesis test for the population proportion, you sample 400 observations that result in 212 successes. Use the p-value approach to conduct the following tests at = 0.01. Use Table 1. H0: p 0.54; HA: p < 0.54. a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic a-2. The p-value is: (Round p-value to 4 decimal places.) 0.025 Picture p-value < 0.05 0.05 Picture p-value < 0.10 p-value Picture 0.10 p-value < 0.01 0.01 Picture p-value < 0.025 a-3. What is the conclusion? Do not reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than . Reject H0 since the p-value is smaller than . Reject H0 since the p-value is greater than . H0: p = 0.54; HA: p 0.54. b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic b-2. The p-value is: (Round p-value to 4 decimal places.) 0.01 Picture p-value < 0.025 0.025 Picture p-value < 0.05 0.05 Picture p-value < 0.10 p-value Picture 0.10 p-value < 0.01 b-3. What is the conclusion? Reject H0 since the p-value is greater than . Reject H0 since the p-value is smaller than . Do not reject H0 since the p-value is greater than . Do not reject H0 since the p-value is smaller than .

Explanation / Answer

here p=0.54 and n=400

std error =(p(1-p)/n)1/2 =0.025

sample proportion phat=212/400 =0.53

therefore a-1) test statistic z=(phat-p)/std error =(0.53-0.54)/0.025=-0.40

a-2) p-value is: >0.10

a-3)Do not reject H0 since the p-value is greater than .

b-1) test statistic. -0.40

b-2) p-value is: >0.10

b-3)  Do not reject H0 since the p-value is greater than .

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