Instruction: Please conduct a hypothesis testing to a given statistic.
Scenario: According to CNN on January 26th in 2016, Donald Trump topped 40% mark for the first time in CNN polling. In this poll, 41 % of the respondents said that they will support for Donald Trump while 19% for Ted Cruz. In this January poll, there seem to be approximately 22% difference between Donald Trump and Ted Cruz. In the sample, there were 1,002 adult Americans interviewed by telephones. Let’s test whether the 22% difference is statistically meaningful or not. Please set up two hypotheses (the null and the alternative) and conduct a hypothesis testing in three different ways: Confidence interval, Test Statistics, and P-value. As a concluding remark, clearly mention the testing result.
| * Hint: Central limit theorem says that the linear combination of random variables is also a random variable. * Difference in proportions: .41 – .22 * Standard error of the difference: square root of [ (.41×.59)/1002 + (.22 × .78)/1002] * Z-score = difference / SE(difference) |
