Math Problem Statement
You may need to use the appropriate technology to answer this question. During the first 13 weeks of the television season, the Saturday evening 8 p.m. to 9 p.m. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 95 homes, CBS 70 homes, NBC 89 homes, and independents 46 homes. Test with 𝛼 = 0.05 to determine whether the viewing audience proportions changed. State the null and alternative hypotheses. H0: pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18 Ha: The proportions are not pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18. H0: pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18 Ha: pABC ≠ 0.29, pCBS ≠ 0.28, pNBC ≠ 0.25, pIND ≠ 0.18 H0: pABC ≠ 0.29, pCBS ≠ 0.28, pNBC ≠ 0.25, pIND ≠ 0.18 Ha: pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18 H0: The proportions are not pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18. Ha: pABC = 0.29, pCBS = 0.28, pNBC = 0.25, pIND = 0.18 Find the value of the test statistic. (Round your answer to three decimal places.) 6.868 Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There has been a significant change in the viewing audience proportions. Do not reject H0. There has been a significant change in the viewing audience proportions. Do not reject H0. There has not been a significant change in the viewing audience proportions. Reject H0. There has not been a significant change in the viewing audience proportions.
Solution
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Math Problem Analysis
Mathematical Concepts
Chi-square test
Hypothesis testing
Probability distributions
Formulas
Chi-square test statistic formula
Calculation of expected frequencies
Theorems
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Suitable Grade Level
Advanced undergraduate or graduate level
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