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##### Statstics exam

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solution

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Question;If a particular batch of data is approximately;normally distributed, we would find that approximately;2 of every 3;observations would fall between +/- 1 standard deviation around the mean.;4 of every 5;observations would fall between +/- 1.28 standard deviations around the mean.;19 of every 20;observations would fall between +/- 2 standard deviations around the mean.;All the above.;Question 6;Suppose a 98% confidence interval for? turns;out to be (1000, 2100). If this interval was based on a sample of size;n=25 explain what assumptions are necessary for this interval to be valid.;The sampling;distribution of the sample mean must have a normal distribution.;The population must;have an approximately normal distribution.;The sampling;distribution must be biased with 24 degrees of freedom.;The population of;salaries must have an approximate t distribution.;Question 7;The mean age of professors at a university is;over 55.3 years. If a hypothesis test is performed, how should you interpret a;decision that fails to reject the null hypothesis?;There is sufficient;evidence to reject the claim? > 55.3.;There is not;sufficient evidence to reject the claim? > 55.3.;There is sufficient;evidence to support the claim? > 55.3.;There is not;sufficient evidence to support the claim? > 55.3;Question 8;Suppose a 95%;confidence interval for? turns out to be (100, 230). To make more useful;inferences from the data, it is desired to reduce the width of the confidence;interval. Which of the following will result in a reduced interval width?;Increase;the sample size and decrease the confidence level.;Decrease;the confidence level.;Increase;the sample size.;Question 10;1.;The level of significance,?, is the probability of making a;Correct;decision;Type;I error;Type;II error;Type;? error;All;of these..;Question 11;1.;The ___________the R2, and the __________ the standard;error, the stronger the relationship between the dependent variable and the;independent variable.;Higher, higher;Higher, lower;Lower, higher;Lower, lower;5 points;Question 12;1.;The intercept (b0) represents;the estimated average;change in Y per unit change in X.;the predicted value of;Y.;variation around the;line of regression.;predicted value of Y;when X = 0.;5 points;Question 13;1.;The results of a survey about a recent judicial;appointment are given in the table below. Describe, in detail, what a;relative frequency histogram would look like. What are the labels on;each axis? What are the values on the y-axis?;Response;Frequency;Strongly Favor;30;Favor;15;Neutral;38;Oppose;13;Strongly Oppose;104;2.;Question 14;1.;Find the standard deviation of the following sample;15;16;17;18;19;2.00;1.41;1.58;1.50;15 points;Question 15;1.;Find P(-1.26? Z? 0.47);0.5318;0.5770;0.4682;0.4230;5 points;Question 16;1.;Find P(Z? 3.02);0.4987;0.9788;0.9987;0.0013;5 points;Question 17;1.;Find z.20.;0.42;-1.28;0.84;0.25;5 points;Question 18;1.;You are offered a choice where you can take a certain amount of $;20 or partake in a gamble, where you put up $30 and have a 50% chance of;winning $50 and 50% chance of winning $10. The decision tree is;drawn for you. What is the expected value at node 2?;Press Tab to enter the;content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor;Use arrow keys to select functions;Bold;Italic;Underline;-- Font family --;Andale Mono;Arial;Arial Black;Book Antiqua;Comic Sans MS;Courier New;Georgia;Helvetica;Impact;Symbol;Tahoma;Terminal;Times New Roman;Trebuchet MS;Verdana;Webdings;Wingdings;Font family;-- Font size --;1 (8pt);2 (10pt);3 (12pt);4 (14pt);5 (18pt);6 (24pt);7 (36pt);Font size;Text Color;?;Bullet List;?;Number List;?;Toggle Spell Checker;?;Insert/Edit;Link;Remove;Link;Bold;Italic;Underline;Strikethrough;-- Format --;Heading;Sub Heading 1;Sub Heading 2;Paragraph;Formatted Code;Format;-- Font family --;Font family;-- Font size --;Font size;Bullet;List;Number;List;Text Color;?;Highlight;?;Remove;Formatting;Cut;Copy;Paste;Find;Undo;Redo;Align;Left;Align;Center;Align;Right;Align;Full;Indent;Outdent;Superscript;Subscript;Insert/Edit;Link;Remove;Link;Direction Left to Right;Direction Right to Left;Line;Horizontal;Rule;Insert Nonbreaking Space Character;Toggle;Spell Checker;Launch;Math Editor;Insert Mashup;?;Show Nonprinting Characters;Blockquote;Symbol;Emotions;Anchor;Insert/Edit;Table;Table;Row Properties;Table Cell Properties;Insert;Row Before;Insert;Row After;Delete;Row;Insert;Column Before;Insert;Column After;Delete;Column;Merge;Table Cells;Split Merged Table Cells;HTML;Code View;Edit;CSS Style;Preview;Help;Full;Screen;Show;More;Path;Words:0;Question 19;1.;You are offered a choice where you can take a certain amount of $;20 or partake in a gamble, where you put up $30 and have a 50% chance of;winning $50 and 50% chance of winning $10. The decision tree is drawn for;you. What should you do--take the $20 or gamble?;Press Tab to enter the;content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor;Use arrow keys to select functions;Bold;Italic;Underline;-- Font family --;Andale Mono;Arial;Arial Black;Book Antiqua;Comic Sans MS;Courier New;Georgia;Helvetica;Impact;Symbol;Tahoma;Terminal;Times New Roman;Trebuchet MS;Verdana;Webdings;Wingdings;Font family;-- Font size --;1 (8pt);2 (10pt);3 (12pt);4 (14pt);5 (18pt);6 (24pt);7 (36pt);Font size;Text Color;?;Bullet List;?;Number List;?;Toggle Spell Checker;?;Insert/Edit;Link;Remove;Link;Bold;Italic;Underline;Strikethrough;-- Format --;Heading;Sub Heading 1;Sub Heading 2;Paragraph;Formatted Code;Format;-- Font family --;Font family;-- Font size --;Font size;Bullet;List;Number;List;Text Color;?;Highlight;?;Remove;Formatting;Cut;Copy;Paste;Find;Undo;Redo;Align;Left;Align;Center;Align;Right;Align;Full;Indent;Outdent;Superscript;Subscript;Insert/Edit;Link;Remove;Link;Direction Left to Right;Direction Right to Left;Line;Horizontal;Rule;Insert Nonbreaking Space Character;Toggle;Spell Checker;Launch;Math Editor;Insert Mashup;?;Show Nonprinting Characters;Blockquote;Symbol;Emotions;Anchor;Insert/Edit;Table;Table;Row Properties;Table Cell Properties;Insert;Row Before;Insert;Row After;Delete;Row;Insert;Column Before;Insert;Column After;Delete;Column;Merge;Table Cells;Split Merged Table Cells;HTML;Code View;Edit;CSS Style;Preview;Help;Full;Screen;Show;More;Path;Words:0;Question 20;1.;You are offered a choice where you can take a certain amount of $;20 or partake in a gamble, where you put up $30 and have a 50% chance of;winning $50 and 50% chance of winning $10. The decision tree is drawn for;you. How much should you expect to make?;Press Tab to enter the;content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor;Use arrow keys to select functions;Bold;Italic;Underline;-- Font family --;Andale Mono;Arial;Arial Black;Book Antiqua;Comic Sans MS;Courier New;Georgia;Helvetica;Impact;Symbol;Tahoma;Terminal;Times New Roman;Trebuchet MS;Verdana;Webdings;Wingdings;Font family;-- Font size --;1 (8pt);2 (10pt);3 (12pt);4 (14pt);5 (18pt);6 (24pt);7 (36pt);Font size;Text Color;?;Bullet List;?;Number List;?;Toggle Spell Checker;?;Insert/Edit;Link;Remove;Link;Bold;Italic;Underline;Strikethrough;-- Format --;Heading;Sub Heading 1;Sub Heading 2;Paragraph;Formatted Code;Format;-- Font family --;Font family;-- Font size --;Font size;Bullet;List;Number;List;Text Color;?;Highlight;?;Remove;Formatting;Cut;Copy;Paste;Find;Undo;Redo;Align;Left;Align;Center;Align;Right;Align;Full;Indent;Outdent;Superscript;Subscript;Insert/Edit;Link;Remove;Link;Direction Left to Right;Direction Right to Left;Line;Horizontal;Rule;Insert Nonbreaking Space Character;Toggle;Spell Checker;Launch;Math Editor;Insert Mashup;?;Show Nonprinting Characters;Blockquote;Symbol;Emotions;Anchor;Insert/Edit;Table;Table;Row Properties;Table Cell Properties;Insert;Row Before;Insert;Row After;Delete;Row;Insert;Column Before;Insert;Column After;Delete;Column;Merge;Table Cells;Split Merged Table Cells;HTML;Code View;Edit;CSS Style;Preview;Help;Full;Screen;Show;More;Path;Words:0;Question 21;1.;A researcher wants to estimate the average price of television;sets sold at Wal-Mart. It is assumed from previous studies that? =;45. To estimate the average price within $10 with 95% confidence, what;sample size should be used?;All that is needed is the answer. However;if you would like the possibility of partial credit, show me your work.;(Don't worry about formatting or symbols.);Question 22;1.;Customers at Ingles have a choice when paying for their groceries.;They may check out and pay using the standard cashier assisted checkout, or;they may use a new U-Scan procedure. In the standard procedure an Ingles;employee scans each item and another employee puts it in a bag and then into;the grocery cart. In the U-Scan procedure the customer scans each item, bags;it, and places the bags in the cart themselves. The U-Scan procedure is;designed to reduce the time a customer spends in the check out line. The store;manger wants to know if the mean checkout time using the standard checkout;method is longer than using the U-Scan. She gathered the following sample;information. The time is measured from when the customer enters the line until;their bags are in the cart. Hence the time includes both waiting in line and;checking out.;Mean (minutes) Standard deviation;(minutes) Sample Size;Standard 5.5 0.4 50;U-Scan 5.3 0.3 100;What are the null and alternative hypotheses;that management would be testing? (Don't worry about formatting your;answer.);Question 23;1.;Customers at Ingles have a choice when paying for their groceries.;They may check out and pay using the standard cashier assisted checkout, or;they may use a new U-Scan procedure. In the standard procedure an Ingles;employee scans each item and another employee puts it in a bag and then into;the grocery cart. In the U-Scan procedure the customer scans each item, bags;it, and places the bags in the cart themselves. The U-Scan procedure is;designed to reduce the time a customer spends in the check out line. The store;manger wants to know if the mean checkout time using the standard checkout;method is longer than using the U-Scan. She gathered the following sample;information. The time is measured from when the customer enters the line until;their bags are in the cart. Hence the time includes both waiting in line and;checking out.;Mean (minutes) Standard deviation;(minutes) Sample Size;Standard 5.5 0.4 50;U-Scan 5.3 0.3 100;If? =.05 and if the Excel output shows;that p-value = 0.0013, would you reject Ho? Why or why not?;Question 24;1.;Customers at Ingles have a choice when paying for their groceries.;They may check out and pay using the standard cashier assisted checkout, or;they may use a new U-Scan procedure. In the standard procedure an Ingles;employee scans each item and another employee puts it in a bag and then into;the grocery cart. In the U-Scan procedure the customer scans each item, bags;it, and places the bags in the cart themselves. The U-Scan procedure is;designed to reduce the time a customer spends in the check out line. The store;manger wants to know if the mean checkout time using the standard checkout;method is longer than using the U-Scan. She gathered the following sample information.;The time is measured from when the customer enters the line until their bags;are in the cart. Hence the time includes both waiting in line and checking;out.;Mean (minutes) Standard deviation;(minutes) Sample Size;Standard 5.5 0.4 50;U-Scan 5.3 0.3 100;Can we conclude that the U-Scan system is;better than the standard checkout?;Question 25;1.;The following data represent the age of batteries (in hours) for a;random sample of 10 full charges on a fifth generation iPod music player;7.3;10.2;12.9;10.8;12.1;6.6;10.2;9;8.5;7.1;2.;The following Excel output was obtained. What is the point estimate of;the population mean?;3.;hours;Mean;9.47;Standard Error;0.676929;Median;9.6;Mode;10.2;Standard Deviation;2.140639;Sample Variance;4.582333;Kurtosis;-1.09156;Skewness;0.190992;Range;6.3;Minimum;6.6;Maximum;12.9;Sum;94.7;Count;10;Confidence;Level(95.0%)Question 26;1.;The following data represent the age of batteries (in hours) for a;random sample of 10 full charges on a fifth generation iPod music player;7.3;10.2;12.9;10.8;12.1;6.6;10.2;9;8.5;7.1;2.;The following Excel output was obtained. Construct a 95% confidence;interval for the mean number of hours the batteries will last in the player.;3.;hours;Mean;9.47;Standard Error;0.676929;Median;9.6;Mode;10.2;Standard Deviation;2.140639;Sample Variance;4.582333;Kurtosis;-1.09156;Skewness;0.190992;Range;6.3;Minimum;6.6;Maximum;12.9;Sum;94.7;Count;10;Confidence;Level(95.0%);1.531321;Question 27;1.;A sample of scores on an examination given in two different;classes is examined. The following Excel output was obtained. Use?;=.05. In order to determine if Class 2 has a different grade from Class;1, what are the null and alternative hypotheses?;t-Test: Two-Sample;Assuming Unequal Variances;class 1;class 2;Mean;78;79;Variance;90;47.333;Observations;9;7;Hypothesized Mean;Difference;0;df;14;t Stat;-0.244;P(T<=t) one-tail;0.405;t Critical one-tail;1.761;P(T<=t) two-tail;0.811;t Critical two-tail;2.145;Question 28;1.;A sample of scores on an examination given in two different;classes is examined. The following Excel output was obtained. Use?;=.05. Exactly what p-value did you use to answer to determine if Class 2;has a different average?;t-Test: Two-Sample;Assuming Unequal Variances;class 1;class 2;Mean;78;79;Variance;90;47.333;Observations;9;7;Hypothesized Mean;Difference;0;df;14;t Stat;-0.244;P(T<=t) one-tail;0.405;t Critical one-tail;1.761;P(T<=t) two-tail;0.811;t Critical two-tail;2.145;2.;Press Tab to enter the;content editor. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Content Editor;Use arrow keys to select functions;Bold;Italic;Underline;-- Font family --;Andale Mono;Arial;Arial Black;Book Antiqua;Comic Sans MS;Courier New;Georgia;Helvetica;Impact;Symbol;Tahoma;Terminal;Times New Roman;Trebuchet MS;Verdana;Webdings;Wingdings;Font family;-- Font size --;1 (8pt);2 (10pt);3 (12pt);4 (14pt);5 (18pt);6 (24pt);7 (36pt);Font size;Text Color;?;Question 29;1.;A sample of scores on an examination given in two different;classes is examined. The following Excel output was obtained. Use?;=.05. Does Class 2 have a different grade?;t-Test: Two-Sample;Assuming Unequal Variances;class 1;class 2;Mean;78;79;Variance;90;47.333;Observations;9;7;Hypothesized Mean;Difference;0;df;14;t Stat;-0.244;P(T<=t) one-tail;0.405;t Critical one-tail;1.761;P(T<=t) two-tail;0.811;t Critical two-tail;2.145;Question 30;1.;Auto, Inc., a fictional automobile manufacturer, is interested in;estimating the value derived from a proposed Strategic Alternative (SA). The;SA, posed by the CEO of the company, is to acquire an elite, high-end auto;company where the average retail price of a car is $80,000. As part of this;task, the acquisition team develops a three-year market analysis to determine;if adequate market demand exists for luxury automobiles. The team chooses to;use the predictive power of regression analysis to help make these projections.;The first step in this process is to understand;what drives total market demand for elite, high-end luxury automobiles. After;analyzing the industry, the group hypothesizes that gross domestic product, or;GDP, is a key predictor of market demand for these automobiles.;To gather historical GDP data, the team turns to;online databases located on the Federal Reserve Board website.To gather data on;new vehicle sales for elite, high-end luxury cars, it uses the Bureau of Labor;Statistics' online databases on new vehicle car sales. (The GDP data is;in billions of dollars and the sales data is in thousands of units.);Is GDP a valid predictor of sales? How do;you know?;SUMMARY OUTPUT;Regression Statistics;Multiple R;0.831453;R Square;0.691314;Adjusted R Square;0.652728;Standard Error;251.102335;Observations;10;ANOVA;df;SS;MS;F;Significance F;Regression;1;1129665.838;1129665.84;17.9163069;0.0028655;Residual;8;504419.0623;63052.3828;Total;9;1634084.9;Coefficients;Standard Error;t Stat;P-value;Intercept;739.44976;519.58568;1.42315;0.19250;GDP (in $billions);0.28527;0.06740;4.23277;0.00287;Question 31;1.;Auto, Inc., a fictional automobile manufacturer, is interested in;estimating the value derived from a proposed Strategic Alternative (SA). The;SA, posed by the CEO of the company, is to acquire an elite, high-end auto;company where the average retail price of a car is $80,000. As part of this;task, the acquisition team develops a three-year market analysis to determine;if adequate market demand exists for luxury automobiles. The team chooses to;use the predictive power of regression analysis to help make these;projections.;The first step in this process is to understand;what drives total market demand for elite, high-end luxury automobiles. After;analyzing the industry, the group hypothesizes that gross domestic product, or;GDP, is a key predictor of market demand for these automobiles.;To gather historical GDP data, the team turns to;online databases located on the Federal Reserve Board website.To gather data on;new vehicle sales for elite, high-end luxury cars, it uses the Bureau of Labor;Statistics' online databases on new vehicle car sales. (The GDP data is;in billions of dollars and the sales data is in thousands of units.);If the GDP is at 12,000 billion dollars, how;many thousands of units of cars would you expect to be sold?;SUMMARY OUTPUT;Regression Statistics;Multiple R;0.831453;R Square;0.691314;Adjusted R Square;0.652728;Standard Error;251.102335;Observations;10;ANOVA;df;SS;MS;F;Significance F;Regression;1;1129665.838;1129665.84;17.9163069;0.0028655;Residual;8;504419.0623;63052.3828;Total;9;1634084.9;Coefficients;Standard Error;t Stat;P-value;Intercept;739.44976;519.58568;1.42315;0.19250;GDP (in $billions);0.28527;0.06740;4.23277;0.00287;Question 32;1.;Auto, Inc., a fictional automobile manufacturer, is interested in;estimating the value derived from a proposed Strategic Alternative (SA). The;SA, posed by the CEO of the company, is to acquire an elite, high-end auto;company where the average retail price of a car is $80,000. As part of this;task, the acquisition team develops a three-year market analysis to determine;if adequate market demand exists for luxury automobiles. The team chooses to;use the predictive power of regression analysis to help make these;projections.;The first step in this process is to understand;what drives total market demand for elite, high-end luxury automobiles. After;analyzing the industry, the group hypothesizes that gross domestic product, or;GDP, is a key predictor of market demand for these automobiles.;To gather historical GDP data, the team turns to;online databases located on the Federal Reserve Board website.To gather data on;new vehicle sales for elite, high-end luxury cars, it uses the Bureau of Labor;Statistics' online databases on new vehicle car sales. (The GDP data is;in billions of dollars and the sales data is in thousands of units.);1.;Interpret b1.;SUMMARY OUTPUT;Regression Statistics;Multiple R;0.831453;R Square;0.691314;Adjusted R Square;0.652728;Standard Error;251.102335;Observations;10;ANOVA;df;SS;MS;F;Significance F;Regression;1;1129665.838;1129665.84;17.9163069;0.0028655;Residual;8;504419.0623;63052.3828;Total;9;1634084.9;Coefficients;Standard Error;t Stat;P-value;Intercept;739.44976;519.58568;1.42315;0.19250;GDP (in $billions);0.28527;0.06740;4.23277;0.00287;1.531321

Paper#62160 | Written in 18-Jul-2015

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