Homework Sourse4 A politician claims that he is supported by a clear majori
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A politician claims that he is supported by a clear majority of voters. In a recent survey, 28 out of 43 randomly selected voters indicated that they would vote for the politician. Use a 10% significance level for the test. Use Table 1.
Select the null and the alternative hypotheses.
Calculate the sample proportion. (Round your answer to 3 decimal places.)
Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)
What is the conclusion?
| A politician claims that he is supported by a clear majority of voters. In a recent survey, 28 out of 43 randomly selected voters indicated that they would vote for the politician. Use a 10% significance level for the test. Use Table 1. |
Solution
(a)H0: p ? 0.50; HA: p > 0.50
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(b)Sample proportion = 28/43 =0.651
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(c) The Test statistic is
Z=(phat-p)/sqrt(p*(1-p)/n)
=(0.651-0.5)/sqrt(0.5*0.5/43)
=1.98
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(d) It is a right-tailed test.
So the p-value= P(Z>1.98) =0.0239 (from standard normal table)
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(e)Reject H0; the politician is supported by a clear majority
