For the week ended January 15, 2009, the bullish sentiment of individual investors was 27.6% (AAII Journal, February 2009). The bullish sentiment was reported to be 48.7% one week earlier and 39.7% one month earlier. The sentiment measures are based on a poll conducted by the American Association of Individual Investors. Assume that each of the bullish sentiment measures was based on a sample size of 240.
a. Develop a 95% confidence interval for the difference between the bullish sentiment measures for the most recent two weeks.
b. Develop hypotheses so that rejection of the null hypothesis will allow us to conclude that the most recent bullish sentiment is weaker than that of one month ago.
c. Conduct a hypotheses test of part (b) using α = .01. What is your conclusion?