A CNN/ ORC poll conducted in January, 2013, asked 814 adults in the United States, “ Which of the following do you think is the most pressing issue facing the country today?” and then presented seven choices, one of which was “The Economy.” (www.pollingreport.com/prioriti.htm, accessed July 16, 2013.) “The Economy” was chosen by 46% of the respondents. Suppose an unscrupulous politician wanted to show that the economy was not a pressing issue, and stated “Significantly fewer than half of adults think that the economy is a pressing issue.”
a. What are the null and alternative hypotheses the politician is implicitly testing in this quote? Make sure you specify the population value being tested and the population to which it applies.
b. Using the results of the poll, find the value of the standardized score that would be used as the test statistic.
c. If you answered parts (a) and (b) correctly, the p-value for the test should be about 0.011. Explain how the politician reached the conclusion stated in the quote.
d. Do you think the statement made by the politician is justified? Explain.