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. Possibleresponses (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.tBrokerageSpeedSatisfactionScottrade, Inc.3.43.5Charles Schwab3.33.4Fidelity Brokerage Services3.43.9TD Ameritrade3.63.7E*Trade Financial3.22.9Vanguard Brokerage Services3.82.8USAA Brokerage Services3.83.6Thịnkorswim2.62.6Wells Fargo Investments2.72.3Interactive Brokers4.04.0Zecco.com2.52.5(a) Develop a scatter diagram for these data with the speed of execution as the independent variable.4.54.5-4.5-4.54.04.0-4.0-4.03.53.53.53.53.03.03.03.02.52.52.52.52.53.03.54.04.52.53.03.54.04.52.53.03.54.04.52.53.03.54.04.5Speed of ExecutionSpeed of ExecutionSpeed of ExecutionSpeed of Execution(b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?O The scatter diagram indicates a negative linear relationship between speed of execution rating and overall satisfaction rating for electronictrades.O The scatter diagram indicates a positive linear relationship between speed of execution rating and overall satisfaction rating for electronic trades.O The scatter diagram indicates no noticeable linear relationship between speed of execution rating and overall satisfaction rating for electronictrades.Satisfaction (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?O The scatter diagram indicates a negative linear relationship between speed of execution rating and overall satisfaction rating for electronictrades.O The scatter diagram indicates a positive linear relationship between speed of execution rating and overall satisfaction rating for electronic trades.O The scatter diagram indicates no noticeable linear relationship between speed of execution rating and overall satisfaction rating for electronictrades.(c) Develop the least squares estimated regression equation. (Round your numerical values to three decimal places.).205 +.908x(d) Provide an interpretation for the slope of the estimated regression equation.O The slope gives the change in the speed of execution rating for every one point increase in the overall satisfaction rating.O The slope gives the change in the overall satisfaction rating for every one point increase in the speed of execution rating.O The slope gives the overall satisfaction rating when the speed of execution rating is 0.O The slope gives the change in the speed of execution rating for every one point decrease in the overall satisfaction rating.O The slope gives the speed of execution rating when the overall satisfaction rating is 0.(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 theoverall satisfaction rating? (Round your answer to one decimal place.)

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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 overal 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 calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow. Brokerage Speed Satisfaction Scottrade, Inc. 3.4 3.5 Charles Schwab 3.3 3.4 Fidelity Brokerage Services 3.4 3.9 TD Ameritrade 3.6 3.7 E"Trade Financial 3.2 2.9 Vanguard Brokerage Services 3.8 2.8 USAA Brokerage Services 3.8 3.6 Thinkorswim 2.6 2.6 Wells Fargo Investments 2.7 2.3 Interactive Brokers 4.0 4.0 Zecco.com 2.5 2.5

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 overal 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 calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow. Brokerage Speed Satisfaction Scottrade, Inc. 3.4 3.5 Charles Schwab 3.3 3.4 Fidelity Brokerage Services 3.4 3.9 TD Ameritrade 3.6 3.7 E"Trade Financial 3.2 2.9 Vanguard Brokerage Services 3.8 2.8 USAA Brokerage Services 3.8 3.6 Thinkorswim 2.6 2.6 Wells Fargo Investments 2.7 2.3 Interactive Brokers 4.0 4.0 Zecco.com 2.5 2.5

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

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.t
Brokerage
Speed
Satisfaction
Scottrade, Inc.
3.4
3.5
Charles Schwab
3.3
3.4
Fidelity Brokerage Services
3.4
3.9
TD Ameritrade
3.6
3.7
E*Trade Financial
3.2
2.9
Vanguard Brokerage Services
3.8
2.8
USAA Brokerage Services
3.8
3.6
Thịnkorswim
2.6
2.6
Wells Fargo Investments
2.7
2.3
Interactive Brokers
4.0
4.0
Zecco.com
2.5
2.5
(a) Develop a scatter diagram for these data with the speed of execution as the independent variable.
4.5
4.5-
4.5-
4.5
4.0
4.0-
4.0-
4.0
3.5
3.5
3.5
3.5
3.0
3.0
3.0
3.0
2.5
2.5
2.5
2.5
2.5
3.0
3.5
4.0
4.5
2.5
3.0
3.5
4.0
4.5
2.5
3.0
3.5
4.0
4.5
2.5
3.0
3.5
4.0
4.5
Speed of Execution
Speed of Execution
Speed of Execution
Speed of Execution
(b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
O The scatter diagram indicates a negative linear relationship between speed of execution rating and overall satisfaction rating for electronic
trades.
O The scatter diagram indicates a positive linear relationship between speed of execution rating and overall satisfaction rating for electronic trades.
O The scatter diagram indicates no noticeable linear relationship between speed of execution rating and overall satisfaction rating for electronic
trades.
Satisfaction

(b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
O The scatter diagram indicates a negative linear relationship between speed of execution rating and overall satisfaction rating for electronic
trades.
O The scatter diagram indicates a positive linear relationship between speed of execution rating and overall satisfaction rating for electronic trades.
O The scatter diagram indicates no noticeable linear relationship between speed of execution rating and overall satisfaction rating for electronic
trades.
(c) Develop the least squares estimated regression equation. (Round your numerical values to three decimal places.)
.205 +.908x
(d) Provide an interpretation for the slope of the estimated regression equation.
O The slope gives the change in the speed of execution rating for every one point increase in the overall satisfaction rating.
O The slope gives the change in the overall satisfaction rating for every one point increase in the speed of execution rating.
O The slope gives the overall satisfaction rating when the speed of execution rating is 0.
O The slope gives the change in the speed of execution rating for every one point decrease in the overall satisfaction rating.
O The slope gives the speed of execution rating when the overall satisfaction rating is 0.
(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? (Round your answer to one decimal place.)

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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. Suppose a portion of the survey results follow. Brokerage Speed Satisfaction A 3.4 3.5 B 3.3 3.5 C 3.4 3.9 D 3.6 3.6 E 3.2 2.9 F 3.8 2.8 G 3.8 3.6 H 2.6 2.6 I 2.7 2.3 J 4.0 4.0 K 2.5 2.5 These ratings data on x = the quality of the speed of execution and y = overall satisfaction with electronic trades provided the estimated regression equation ŷ = 0.243 + 0.896x. At the 0.05 level of…
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