Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

The manager of a local fast-food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink from the beverage fountain instead of filling it with water. The manager selected a random sample of 50 customers who asked for a water cup when placing an order and found that 8 of those customers filled the cup with a soft drink from the beverage fountain.

(a) Find the sample size, and the proportion of customers who ordered water and took a soft drink (�). Are the conditions for the normal curve satisfied? Show your calculations.

(b) Construct a 98% confidence interval for the proportion of all customers who, having asked for a water cup with their order, will fill the cup with a soft drink from the beverage fountain.

(c) If we want to cut the width of the confidence interval in half (keeping the same confidence level and assuming the sample proportion will be the same), how many customers will we have to sample?

Tennindo, Inc. is starting up its​ new, cost-efficient gaming system​ console, the yuu. Tennindo currently has 3 comma 500 ​cash-paying customers and makes a profit of ​$60 per unit. Tennindo wants to expand its customer base by allowing customers to buy on credit. It estimates that credit sales will bring in an additional 1 comma 000 customers per​ year, but that there will also be a default rate on credit sales of 5​%. It costs ​$250 to make a​ yuu, which retails for ​$310. If all customers​ (old and​ new) buy on​ credit, what is the cost of bad debt without credit​ screening? What is the most Tennindo would pay for credit screening that accurately identifies​ bad-debt customers prior to the​ sale? What are the increased profits from adding credit sales for customers with and without credit​ screening? Should Tennindo offer credit sales if credit screening costs ​$10 per​ customer?

Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

Use your knowledge about price-searching firms and two-part pricing to advise the company below.

The company has a bar and is trying to decide on the cover charge (if any) and price for each drink. It has done a modest survey to ask customers to classify themselves as light drinkers or heavy drinkers and to indicate the number of drinks they would typically consume during the evening at various possible prices.

The estimate from the study is that a change in the price equal to $1 per drink causes light drinkers to change their consumption on average by 0.5 drinks per night. However, a change in price of $1 causes heavy drinkers to change their consumption on average by 1.0 drink per night. For both groups a typical consumer will not consume anything once the price reaches $9 per drink. (Customers might instead go to another bar or not go to a bar at all.)

(Note the distinction between dQ/dP and dP/dQ, which is its inverse.) Draw an inverse demand curve for a typical light drinker and for a typical heavy drinker on the same diagram. Explain your diagram. Write equations for the curves in slope-intercept form.

If 300 people visit the bar on a typical evening, with 200 people being light drinkers and 100 people being heavy drinkers, draw an overall (inverse) demand curve for all of the consumers combined. (A good way to start is with a price of $9. Then determine what would happen if the price were reduced all the way to zero. You would then be able to plot on a diagram the total quantity demanded at $9 and the total quantity demanded at $0. Connect the two points involved with a straight line and determine its slope.)

What is the slope and what is the intercept for this (total) demand curve? Write an equation in slope-intercept form.

Recall that, in the case of a straight-line demand curve, the slope of the marginal revenue line for a company that does not practice price discrimination is double the slope of the (total) market demand curve.        

If the marginal cost of making drinks (the alcohol, the bartender’s labor, and the amortized cost of purchasing glasses and cleaning them repeatedly) is constant at $5 per drink, and if no cover charge is assessed, what is the best price to charge for drinks? How many drinks would be sold on a typical evening? What would your profits be? Show your work. What would be the point price elasticity of demand at the profit-maximizing price? (Find the quantity where marginal revenue equals marginal cost, and then use your equation for the total demand curve to determine the price to charge.)

However, our last two-part pricing slide tells us that a monopoly user charge is too high from the standpoint of two-part pricing. If you cut your price by $1 per drink AND assess the maximum possible cover charge without causing a typical light drinker to refuse to enter the bar, would your profits improve? How high would the cover charge be? Calculate both the cover charge and your total profits. Would the new pricing increase profits? Show your work.

(Using calculus). Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, PLUS 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.)

You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every ‘Q’ that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually you can solve for the exact best P, Q, and cover charge.  

Use your knowledge about price-searching firms and two-part pricing to advise the company below.

The company has a bar and is trying to decide on the cover charge (if any) and price for each drink. It has done a modest survey to ask customers to classify themselves as light drinkers or heavy drinkers and to indicate the number of drinks they would typically consume during the evening at various possible prices.

The estimate from the study is that a change in the price equal to $1 per drink causes light drinkers to change their consumption on average by 0.5 drinks per night. However, a change in price of $1 causes heavy drinkers to change their consumption on average by 1.0 drink per night. For both groups a typical consumer will not consume anything once the price reaches $9 per drink. (Customers might instead go to another bar or not go to a bar at all.)

(Note the distinction between dQ/dP and dP/dQ, which is its inverse.) Draw an inverse demand curve for a typical light drinker and for a typical heavy drinker on the same diagram. Explain your diagram. Write equations for the curves in slope-intercept form.

If 300 people visit the bar on a typical evening, with 200 people being light drinkers and 100 people being heavy drinkers, draw an overall (inverse) demand curve for all of the consumers combined. (A good way to start is with a price of $9. Then determine what would happen if the price were reduced all the way to zero. You would then be able to plot on a diagram the total quantity demanded at $9 and the total quantity demanded at $0. Connect the two points involved with a straight line and determine its slope.)

What is the slope and what is the intercept for this (total) demand curve? Write an equation in slope-intercept form.

Recall that, in the case of a straight-line demand curve, the slope of the marginal revenue line for a company that does not practice price discrimination is double the slope of the (total) market demand curve.        

If the marginal cost of making drinks (the alcohol, the bartender’s labor, and the amortized cost of purchasing glasses and cleaning them repeatedly) is constant at $5 per drink, and if no cover charge is assessed, what is the best price to charge for drinks? How many drinks would be sold on a typical evening? What would your profits be? Show your work. What would be the point price elasticity of demand at the profit-maximizing price? (Find the quantity where marginal revenue equals marginal cost, and then use your equation for the total demand curve to determine the price to charge.)

However, our last two-part pricing slide tells us that a monopoly user charge is too high from the standpoint of two-part pricing. If you cut your price by $1 per drink AND assess the maximum possible cover charge without causing a typical light drinker to refuse to enter the bar, would your profits improve? How high would the cover charge be? Calculate both the cover charge and your total profits. Would the new pricing increase profits? Show your work.

(Using calculus). Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, PLUS 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.)

You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every ‘Q’ that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually you can solve for the exact best P, Q, and cover charge.

A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.)

Click here for the Excel Data File

a. Calculate the grand mean. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.

• H₀: μ_A = μ_B = μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≤ μ_B ≤ μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≥ μ_B ≥ μ_C; H_A: Not all population means are equal.

e-1. Calculate the value of the F_{(df1, df2)} test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

e-2. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

f. At the 1% significance level, what is the conclusion to the test?

• Do not reject H₀ since the p-value is not less than significance level.

• Reject H₀ since the p-value is less than significance level.

• Reject H₀ since the p-value is not less than significance level.

• Do not reject H₀ since the p-value is less than significance level.

g. Interpret the results at αα = 0.01.

• We conclude that some means differ.

• We cannot conclude that some means differ.

• We cannot conclude that all means differ.

• We cannot conclude that population mean C is greater than population mean A.

rev: 06_10_2019_QC_CS-170121

A researcher is interested in whether the phonics method of teaching reading is more or less effective than the sight method, depending on what grade the child is in. Twenty children were randomly selected from each of three grades: kindergarten (K), first grade (1), and second grade. Achievement was measured in terms of reading comprehension where higher scores indicate better comprehension. Within each grade, 10 children were assigned to each of two methods of teaching reading - phonics or sight. The data are as follows: Grade Levels K 1 2 K 1 2 14 25 49 17 35 34 20 29 49 22 36 33 16 27 46 19 40 34 Sight 21 31 46 Phonics 20 34 39 20 27 44 26 37 38 14 34 43 18 41 33 21 32 50 26 42 35 23 34 43 18 33 42 14 35 48 25 34 42 15 28 52 23 43 38 a. State the Null hypotheses for each main effect and interaction – 5 points a. The different methods for teaching reading do not show a significant difference. b. Present the means and SD for each level of each factor– 5 points c. Test the null hypothesis for both main effects and interactions and present the ANOVA source table with all relevant statistics– 15 points. Tests of Between-Subjects ANOVA source Table Dependent Variable: RC Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared method grade method * grade Error Total Corrected Total a. R Squared = (Adjusted R Squared = . Sig = 0 means p is < .001. SPSS takes out the probability value to 8 decimals. So, reporting Sig as .000 means the probability (p) is less than or below the .001 level. d. Specify all variables– 5 points. e. Compute, report and explain results from the HSD post hoc follow-up test– 10 points.. f. Present a graph of the interaction of the two factors– 5 points. g. Write a statement as to your conclusions– 5 points..

A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.)

Click here for the Excel Data File

a. Calculate the grand mean. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.

• H₀: μ_A = μ_B = μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≤ μ_B ≤ μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≥ μ_B ≥ μ_C; H_A: Not all population means are equal.

e-1. Calculate the value of the F_{(df1, df2)} test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

e-2. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

f. At the 1% significance level, what is the conclusion to the test?

• Do not reject H₀ since the p-value is not less than significance level.

• Reject H₀ since the p-value is less than significance level.

• Reject H₀ since the p-value is not less than significance level.

• Do not reject H₀ since the p-value is less than significance level.

g. Interpret the results at αα = 0.01.

• We conclude that some means differ.

• We cannot conclude that some means differ.

• We cannot conclude that all means differ.

• We cannot conclude that population mean C is greater than population mean A.

The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.

(a)

Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let μ₁ = population mean minutes late for delayed Company A flights and μ₂ = population mean minutes late for delayed Company B flights.)

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

(b)

What is the sample mean number of minutes late for delayed flights for each of these two airlines?

Company A min

Company B   min

(c)

Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Do not reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.  

Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.

Do not Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.