Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

d. Provide an interpretation for the slope of the estimated regression equation.

Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

c. Develop the least squares estimated regression equation.

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 bullish on the stock market.

Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

a. Develop a scatter diagram for these data with the room rate as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $\$128$, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

e. Suppose Zecco.com developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current

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 neutral on the stock market.

A sample containing years to maturity and yield (%) for 40 corporate bonds is contained in the data file named CorporateBonds (Barron's, April 2, 2012).

a. Develop a scatter diagram of the data using x=years to maturity as the independent variable. Does a simple linear regression model appear to be appropriate?

b. Develop an estimated regression equation with x=years to maturity and $x^2$ as the independent variables.

c. As an alternative to fitting a second-order model, fit a model using the natural logarithm of price as the independent variable; that is, $\hat{y}=b_0+b_1 \ln (x)$. Does the estimated regression using the natural logarithm of x provide a better fit than the estimated regression developed in part (b)? Explain.

A sample containing years to maturity and yield for 40 corporate bonds is contained in the file CorporateBonds.

What is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?

A sample containing years to maturity and yield for 40 corporate bonds is contained in the file CorporateBonds.

Develop a 95% confidence interval for the population mean years to maturity.

The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (l), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website).

$$\begin{array}{lcc} \text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5 \end{array}$$

a. Develop a scatter diagram for these data with the speed of execution as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Develop the least squares estimated regression equation.
d. Provide an interpretation for the slope of the estimated regression equation.
e. Suppose Zecco.com developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of $2.5$ to the average speed of execution rating for the other $10$ brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

The American Association of Individual Investors conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. For the week ending November 7, 2012, the survey results showed 35.0% bullish, 38.6% neutral, and 26.4% bearish. Assume these results are based on a sample of 300 AAII members

Over the long term, the proportion of bearish AAII members is .30. Conduct a hypothesis test at the 1% level of significance to see if the current sample results show that bearish sentiment is below its long term average of .30. What are your findings?

Consider the follow ing hypothesis test.

$$\begin{aligned} & H_0: \mu \geq 10 \\ & H_{ a }: \mu<10 \end{aligned}$$

The sample size is 120 and the population standard deviation is assumed known with $\sigma=5$. Use $\alpha=.05$

What is the probability of making a Type II error if the actual population mean is $8 ?$

An American Society of Investors survey found 30 percent of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability: a. Exactly two of the sampled individuals have used a discount broker? b. Exactly four of them have used a discount broker? c. None of them have used a discount broker?