Suppose for your company, the probability an individual customer purchases something in-store is 0.74. The probability he or she purchases something online is 0.81. We have described a set of Bernoulli trials with this scenario:

            (a) There are two outcomes – purchase (a “success”) or no purchase,

            (b) The probability of a success is constant across trials, and

(c) Trials are independent of each other, assuming customers are not related or shopping together.

(1) What is the expected number of customers until the first one purchases something in-store?

(2) What is the expected number of customers until the first one purchases something online?

(3) What is the probability that the third customer is the first to purchase something in-store?

(4) What is the probability that the fifth customer is the first to purchase something online?

(5) What is the probability of exactly 7 of the next 12 customers purchasing something in-store?

(6) What is the probability that exactly 7 of the next 12 customers will purchase something online?

(7) What is the probability that no more than 6 of the next 9 customers will purchase something in-store?

(8) What is the probability that at least 8 of the next 11 customers will purchase something online?

Now we want to look at purchasing a specific item. Suppose the probability customers purchase that item in-store is 0.60, while the probability they purchase it online is 0.79.

(9) What is the probability exactly 4 out of the next 7 in-store customers will purchase that item?

(10) What is the probability at least 5 of the next 8 online customers will purchase that item?

(11) What is the probability the 4^th in-store customer will be the first to purchase that item?

(12) What is the probability no more than 5 of the next 11 online customers will purchase that item?

(13) What is the probability that at least 8 of the next 12 in-store customers will purchase that item?

(14) What is the probability the first online customer to purchase that item will be before the 5^th?

Suppose for your store, the mean number of customers at any time of the day is 4.8 (this would be λ). Determine the following probabilities. NOTE these are not based on Bernoulli trials.

(15) What is the probability of having no customers in the store at some point during the day?

(16) What is the probability of having at least 6 customers in the store at any given point?

(17) What is the probability of having no more than three customers in the store at any given point?

(18) What is the probability of having exactly 5 customers in the store at any given point?

(19) If I wanted to know the number of customers before the first one bought something, which model would I use?

            GEOMETRIC            BINOMIAL                POISSON            (circle one)

(20) If I wanted to know how many customers out of a certain number will buy something, which model would I use?

            GEOMETRIC            BINOMIAL                POISSON            (circle one)

Question 1

a) For the data in Homework 2, Question 1, calculate the ANOVA table. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

b) Give a 95% confidence interval for the mean sale price for 2000 sq. ft. houses.

c)   Give a 95% prediction interval for the sale price of an individual 2000 sq. ft. house.

d)   For the data in Homework 2, Question 2, calculate the ANOVA table for the data. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

Question 2

A research firm collected data on a sample of n = 30 drivers to investigate the relationship between the age of a driver and the distance the driver can see. The data is given below:

Use SAS to fit a simple linear regression and answer the following questions:

a) Find the least squares estimate for the regression line Y_i = b₀ + b₁X_i + e_i.

b) Estimate the standard deviation of the error term e_i

c)   Test the null hypothesis that b₁ = 0, using α = 0.05. Is the model useful?

d)   Calculate R²? Explain what this means, and comment on whether or not it suggests the model is good.

e)   Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good.

f)    What would you expect the distance that a 50 year old driver can see to be?

g)   Give a 95% prediction interval for the distance that an individual 50 year old can see.

h) Give a 95% confidence interval for the mean distance that 50 year olds can see.

The objective of the question is to test the Hypothesis If the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A. First you must find the mean and standard deviations. Then perform and list the complete required steps for the TWO required Hypothesis tests and ALSO USE THE P-VALUE AS A REJECTION RULE FOR BOTH TESTS.

One Hypothesis test is an F test for the equality of the variances of travel Times and the second test is a T test for the equality of the means of travel times in minutes. The F test must be performed first in order to select either Case1 or Case 2 for the T-test. PLEASE SHOW HOW YOU OBTAINED ALL ANSWERS

Recorded Time values in minutes from point A to point B: 32, 34, 51, 30, 29, 35, 36, 29, 32, 29, 33, 32, 29, 30, 33, 30, 30, 33, 30, 31, 35, 35, 34, 32, 33, 33, 31, 33, 34, 30, 30, 29, 34, 32, 36, 29, 30, 32, 30, 33, 31

Recorded Time values in minutes from point B to point A: 36, 28, 48, 28, 27, 54, 34, 29, 26, 34, 33, 42, 29, 34, 31, 48, 27, 42, 28, 45, 26, 43, 32, 41, 30, 36, 27, 44, 29, 29, 35, 26, 31, 28, 27, 28, 32, 41, 34, 28, 31

The objective of the question is to test the Hypothesis If the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A. First you must find the mean and standard deviations. Then perform and list the complete required steps for the TWO required Hypothesis tests and use the P-Value as a rejection Rule for both tests.

One Hypothesis test is an F test for the equality of the variances of travel Times and the second test is a T test for the equality of the means of travel times in minutes. The F test must be performed first in order to select either Case1 or Case 2 for the T-test.

Recorded Time values in minutes from point A to point B in minutes: 32, 34, 51, 30, 29, 35, 36, 29, 32, 29, 33, 32, 29, 30, 33, 30, 30, 33, 30, 31, 35, 35, 34, 33, 31, 34, 30, 30, 29, 34, 32, 35, 29, 30, 32, 30, 33, 31

n_A=38

Recorded Time values in minutes from point B to point A in minutes: 36, 28, 48, 28, 27, 54, 34, 29, 26, 34, 33, 42, 29, 34, 31, 4, 27, 42, 28, 45, 26, 43, 32, 30, 27, 29, 29, 35, 26, 31, 28, 27, 28, 32, 41, 34, 28, 31

n_B=38

Test the Hypothesis If the Mean travel time in minutes between Point A to Point B is equal to the mean of the travel time in minutes from Point B to your A. First you must find the mean and standard deviations. Then perform and list the complete required steps for the TWO required Hypothesis tests and ALSO USE THE P-VALUE AS A REJECTION RULE FOR BOTH TESTS. One Hypothesis test is an F test for the equality of the variances of travel Times and the second test is a T test for the equality of the means of travel times in minutes. The F test must be performed first in order to select either Case1 or Case 2 for the T-test. PLEASE SHOW HOW YOU OBTAINED ALL ANSWERS

Recorded Time values in minutes from point A to point B: 32, 34, 51, 30, 29, 35, 36, 29, 32, 29, 33, 32, 29, 30, 33, 30, 30, 33, 30, 31, 35, 35, 34, 32, 33, 33, 31, 33, 34, 30, 30, 29, 34, 32, 36, 29, 30, 32, 30, 33, 31

n1=41

Recorded Time values in minutes from point B to point A: 36, 28, 48, 28, 27, 54, 34, 29, 26, 34, 33, 42, 29, 34, 31, 48, 27, 42, 28, 45, 26, 43, 32, 41, 30, 36, 27, 44, 29, 29, 35, 26, 31, 28, 27, 28, 32, 41, 34, 28, 31

n2=41

VF is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statements. Every December, VF sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 24 years of experience, VF categorizes their cases into the following groups:

• Group 1 (new customers, easy): 15 percent of cases
• Group 2 (new customers, complex): 6 percent of cases
• Group 3 (repeat customers, easy): 55 percent of cases
• Group 4 (repeat customers, complex): 24 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation.

In order to prepare the income tax statement, VF needs to complete the following set of activities. Processing times (and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following processing times are expressed in minutes per income tax statement.

The activities are carried out by the following three persons:

• Administrative support person: filing and writing.
• Senior accountant (who is also the owner): initial meeting, review by senior accountant.
• Junior accountant: preparation.

Assume that all three persons work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 60 income tax statements arriving each month.

A.  What is the (implied) utilization of the senior accountant? The junior accountant? The administrative support person? (Round the answers to 3 decimal places.)

Firms grant credit to customers as a way to increase sales. However, granting credit also exposes the firm to the risk of uncollectible accounts. List and describe three actions a firm can take to reduce the risk of bad debt expense. For each action listed, describe the potential costs involved with these steps.

Assume that you are employed in the marketing department for a firm that is producing an electric scooter. In developing this product, you realize that it is important to provide a core product, an actual product, and an augmented product that meets the needs of customers. Develop an outline of how your firm might provide these three product layers in the electric scooter.

On their farm, the Friendly family grows apples that they harvest each fall and make into three products—apple butter, applesauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2 weeks in October. Their three primary resources are cooking time in their kitchen, their own labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5 hours to cook a 10-gallon batch of apple butter, 5.2 hours to cook 10 gallons of applesauce, and 2.8 hours to cook 10 gallons of jelly. A 10-gallon batch of apple butter requires 1.2 hours of labor, a batch of sauce takes 0.8 hour, and a batch of jelly requires 1.5 hours. The Friendly family has 240 hours of labor available during the fall. They produce about 6,500 apples each fall. A batch of apple butter requires 40 apples, a 10-gallon batch of applesauce requires 55 apples, and a batch of jelly requires 20 apples. After the products are canned, a batch of apple butter will generate $190 in sales revenue, a batch of applesauce will generate a sales revenue of $170, and a batch of jelly will generate sales revenue of $155. The

There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations.

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance..