The American Association of Individual Investors (AAII) polls its subscribers on a weekly basis to determine the number who are bullish, bearish, or neutral on the short-term prospects for the stock market. Their findings for the week ending March 2, 2006, are consistent with the following sample results (AAII website, March 7, 2006).

$$\text{Bullish} ~~ 409 ~~~~~~~\text{Neutral} ~~ 299~~~~~~~ \text{Bearish}~~ 291$$

Develop a point estimate of the following population parameters.

The proportion of all AAII subscribers who are bearish on the stock market.

For the week ended January 15, 2009, the bullish sentiment of individual investors was 27.6% (AAIIJournal,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 con- ducted by the American Assocation of Individual Investors. Assume that each of the bull- ish 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 $\alpha$ = .01. What is your conclusion?

For the week ended January 15, 2009, the bullish sentiment of individual investors was 27.6% (AAII Jouranl, 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 Assocation 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 $\alpha$= .01. What is your conclusion?

The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows.

$$\begin{matrix} \text{Kitchen} & \text{Master Bedroom} & \text{Kitchen} & \text{Master Bedroom}\\ \text{25.2} & \text{18} & \text{23} & \text{17.8}\\ \text{17.4} & \text{22.9} & \text{19.7} & \text{24.6}\\ \text{22.8} & \text{26.4} & \text{16.9} & \text{21}\\ \text{21.9} & \text{24.8} & \text{21.8}\\ \text{19.7} & \text{26.9} & \text{23.6}\\ \end{matrix}$$

Develop a 90% confidence interval for the difference between the two population means.

The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost in thousands of dollars for two types of remodeling projects are as follows.

$$\begin{matrix} \text{Kitchen} & \text{Master Bedroom} & \text{Kitchen} & \text{Master Bedroom}\\ \text{25.2} & \text{18} & \text{23} & \text{17.8}\\ \text{17.4} & \text{22.9} & \text{19.7} & \text{24.6}\\ \text{22.8} & \text{26.4} & \text{16.9} & \text{21}\\ \text{21.9} & \text{24.8} & \text{21.8}\\ \text{19.7} & \text{26.9} & \text{23.6}\\ \end{matrix}$$

Develop a point estimate of the difference between the population mean remodeling costs for the two types of projects.

During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest (CNN Headline News, September 30, 2003). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of 2003. The sample mean shows the mean duration of the games included in each sample.

$$\begin{aligned} & 2002 \text { Season } \\ n _ { 1 } = & 60 \\ \overline { x } _ { 1 } = & 2 \text { hours, } 52 \text { minutes } \end{aligned}$$

$$\begin{aligned} & 2003 \text { Season } \\ n _ { 2 } & = 50 \\ \overline { x } _ { 2 } & = 2 \text { hours, } 46 \text { minutes } \end{aligned}$$

Provide a 95% confidence interval estimate of the reduction in the mean duration of games during the 2003 season.