Customers using a self-service soda dispenser take an average of 12 ounces of soda with an SD of 4 ounces. Assume that the amount would be normally distributed.

What is the probability that a randomly selected customer takes over 8 ounces of soda?

0.25

0.84   

0.95

0.75

0.66

What is the probability that a randomly selected customer takes between 14 to 16 ounces of soda?

0.17

0.24   

0.14

0.15

0.85

How many of the next 100 customers will take an average of less than 12.48 ounces?

54

70

33

45

5

Suppose retailers would like to forecast the percentage of customers who plan to purchase gift cards during the upcoming holiday season. The following data show this percentage from 2002 to 2009. The data is as follows:

Year	Percent
2002	55
2003	60
2004	64
2005	67
2006	66
2007	69
2008	66
2009	64

Perform the following:

1. Using a 3-period simple moving average, forecast the percentage of holiday shoppers who will purchase a gift card in 2010.

-

2. Calculate the MAD for the forecast in part a.

3. Using a 3-period weighted moving average with the weights 5, 3, and 1, forecast the percentage of holiday shoppers who will purchase a gift card in 2010.

4. Calculate the MAD for the forecast in part c.

5. In which forecast do you have the most confidence?

10. (12%) Keno: Keno game is a game with 80 numbers 1, 2, … , 80 where 20 numbered balls out of these 80 numbers will be picked randomly. You can pick 4, 5, 6, or 12 numbers as shown in the attached Keno payoff / odds card. When you pick 4 numbers, there is this 4-spot special that you place $2.00 in the bet, and you are paid $410 if all your 4 numbers are among the 20 numbers, or your are paid $4.00 if 3 of the 4 numbers are among the 20 numbers chosen from the 80 numbers. The number of ways of picking 20 numbers from 80 is C(80, 20) = 80! / (60! 20!). The number of ways that all your 4 numbers are among the 20 numbers is: C(76, 16) (why?) = 76! / (60! 16!). The probability that your 4 numbers bingo is C(76, 16) / C(80, 20), and the theoretical payoff should be C(80, 20) / C(76, 16) = 80! * 16! / (76! * 20!) = (80 * 79 * 78 * 77 ) / (20 * 19 * 18 * 17 ) = $326.4355… (a) (6%) Based on this computation, is the payoff fair? Explain! (b) (6%) The payoff for 3 numbers in your 4 chosen numbers appear in the 20 numbers is $4.00. Is that a fair payoff (how is the number of ways of 3 numbers matching related to the number of ways of 4 numbers matching?)?

Find a point on a given line such that if it is joined to two given points on opposite sides of the line, then the angle formed by the connecting segment is bisected by the given line.

A professional football team is preparing its budget for the next year. One component of the budget is the revenue that they can expect from ticket sales. The home venue, Dylan Stadium, has five different seating zones with different prices. Key information is given below. The demands are all assumed to be normally distributed. Seating Zone Seats Available Ticket Price Mean Demand Standard Deviation First Level Sideline 15,000 $1000.00 14,500 750 Second Level 5,000 $90.00 4,750 500 First Level End Zone 10,000 $80.00 9,000 1,250 Third Level Sideline 21,000 $70.00 17,000 2,500 Third Level End Zone 14,000 $60.00 8,000 3,000 Determine the distribution of total revenue under these assumptions using 250 trials. Summarize the statistical results. The question is from following book and from Chapter 12 question 17 Textbook: James Evans, Business Analytics, 3nd edition, 2019, Pearson Education, Pearson. ISBN: 13:978-0-13-523167-8

A quality survey asked recent customers of their experience at a local department store. One question asked for the customers rating on their service using categorical responses of average, outstanding, and exceptional. Another question asked for the applicant’s education level with categorical responses of Some HS, HS Grad, Some College, and College Grad. The sample data below are for 700 customers who recently visited the department store. Education Quality Rating Some HS HS Grad Some College College Grad Average 55 80 50 35 Outstanding 60 105 65 70 Exceptional 35 65 35 45 Using a level of significance of 0.01, is there evidence to suggest that the customer’s Education level and Quality Rating are independent? In other words, is there a relationship or is there NO relationship between Education and Quality Rating? a. State the Null and Alternative hypothesis. b. What is the statistic you would use to analyze this? c. State your decision rule: d. Show your calculation: e. What is your conclusion? Quality Rating and Education level are independent OR Quality Rating and Education level are NOT independent

5. Four different paints are advertised to have the same drying times. To verify the manufacturer’s claim, seven samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Below are the results which may be imported into MSExcel for analysis: (Assume the populations are normally distributed, the populations are independent and the population variances are equal) Paint 1 Paint 2 Paint 3 Paint 4 120 120 117 128 112 130 122 131 121 121 123 131 118 126 115 129 118 126 123 127 121 114 126 126 118 117 126 137 a. Write the Null and Alternative hypothesis to test whether there is a difference in dry time between the samples of each paint? b. What statistic would you use to analyze this? c. At a 0.01 level of significance, what would be your decision rule? d. From your analysis, is there a difference between drying times? e. If there was a difference in dry times how would you determine which paint has the different drying time? (i.e. what formula would you use and what is your decision criteria?) (this is not asking for a calculation)

In​ 2008, the per capita consumption of soft drinks in Country A was reported to be 19.35 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally​ distributed, with a mean of 19.35 gallons and a standard deviation of 4 gallons. Complete parts​ (a) through​ (d) below.

a. What is the probability that someone in Country A consumed more than 14 gallons of soft drinks in​ 2008? The probability is nothing. ​(Round to four decimal places as​ needed.)

b. What is the probability that someone in Country A consumed between 9 and 10 gallons of soft drinks in​ 2008? The probability is nothing. ​(Round to four decimal places as​ needed.)

c. What is the probability that someone in Country A consumed less than 10 gallons of soft drinks in​ 2008? The probability is nothing. ​(Round to four decimal places as​ needed.)

d. 97​% of the people in Country A consumed less than how many gallons of soft​ drinks? The probability is 97​% that someone in Country A consumed less than nothing gallons of soft drinks. ​(Round to two decimal places as​ needed.)

Data from 1991 General Social Survey classify a sample of Americans according to their gender and their opinion about afterlife (example from A. Agresti, 1996, “Introduction to categorical data analysis”). The opinions about afterlife were classified into two categories: Yes and No (or undecided). For example, for the females in the sample - 435 said that they believed in an afterlife and 147 said that they did not or were undecided.

Gender	Belief in Afterlife
	Yes	No or Undecided
Females	435	147
Males	375	134

Estimate the proportion of females who believed in an afterlife (Use a 95% Confidence Interval).

Sample proportion:
Std error for sample proportion
Confidence interval:
Lower boundary
Upper boundary

Test hypothesis that the majority of females (that is, more than 50% females) believed in an afterlife.

- Using a z-score test

Null hypothesis
Research hypothesis
Value of the test statistics
Critical value used in your decision making
State your conclusion

Using c² test

Categories	Expected ps	Expected frequencies	Observed frequencies	Chie-square calculations
Yes
No

Null hypothesis
Research hypothesis
Value of the test statistics
Critical value used in your decision making
State your conclusion

4. Are biomedical engineering salaries in Miami less than those in Minnesota? Salary data show that staff biomedical engineers in Miami earn less than those in Minnesota. Suppose that in a follow-up study of 35 staff engineers in Miami and 45 staff engineers in Minnesota you obtain the following results: Miami Minnesota n1 = 35 n2 = 45 1 = $64, 150 1 = $65, 450 s1 = $2000 s2 = 2500 a. Formulate a hypothesis statement so that if the null hypothesis is rejected, we can conclude that Miami biomedical engineering salaries are significantly lower than those in Minnesota. b. The standard deviations for both populations can be assumed equal, write out the statistic you would use. c. What would be your decision rule? (Use α = 0.05) d. What is the value of your statistic? e. What is your p-value? f. What is your conclusion?

(SHOW WORK)

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c).

​(a) What sample size should be obtained if he wants to be within

44

percentage points with

9494​%

confidence if he uses an estimate of

4848​%

obtained from a​ poll?The sample size is

nothing.

​(Round up to the nearest​ integer.)​(b) What sample size should be obtained if he wants to be within

44

percentage points with

9494​%

confidence if he does not use any prior​ estimates?The sample size is

nothing.

​(Round up to the nearest​ integer.)

​(c) Why are the results from parts​ (a) and​ (b) so​ close?

A.The results are close because the margin of error

44​%

is less than​ 5%.

B.The results are close because

0.48 left parenthesis 1 minus 0.48 right parenthesis equals0.48(1−0.48)=0.24960.2496

is very close to 0.25.

C.The results are close because the confidence

9494​%

is close to​ 100%.

You are preparing some sweet potato pie for your annual Thanksgiving feast. The store sells sweet potatoes in packages of 6. From prior experience you have found that the package will contain 0 spoiled sweet potatoes about 65% of the time, 1 spoiled sweet potato 25% of the time and 2 spoiled sweet potatoes the rest of the time. Conduct a simulation to estimate the number of packages of sweet potatoes you need to purchase to have three dozen (36) unspoiled sweet potatoes.

Part 1 of 3: (6 pts)

Describe in detail and in paragraph form how you will use the random numbers provided from a random number table (in part 2) to conduct 2 trials of this simulation. Be sure to include all of the first four steps of a simulation. Steps 5 and 6 are part 2 and step 7 are part 3 of this question.

1. Identify the component to be repeated.

2. Explain how you will model the outcome.

3. Explain in detail how you will simulate the trial.

4. State clearly what the response variable is.

Part 2 of 3: (3 pts)

Use the random number table to complete 2 trials. Analyze your response variable.

Trial#1:   41  23  19  98  75  08  63  29  10

Trial #2: 88 26 95  69  57  71  02 62 34

Part 3 of 3: (1 pt)

Give your conclusion based on your simulation results.

Each observation in a random sample of 106 bicycle accidents resulting in death was classified according to the day of the week on which the accident occurred. Data consistent with information are given in the following table. Based on these data, is it reasonable to conclude that the proportion of accidents is not the same for all days of the week? Use α = 0.05. (Round your answer to two decimal places.)

Day of Week	Frequency
Sunday	17
Monday	13
Tuesday	13
Wednesday	15
Thursday	17
Friday	18
Saturday	13

χ² =  

P-value interval

p < 0.001

0.001 ≤ p < 0.01    

0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

The proportion of accidents is  ---Select--- the same, not the same for all days.

Could you please explain to me when I should use the two proportion tests?

A two proportion f test tests variance/standard deviation. So if it is testing how much the two proportions vary then isn't it doing what a linear regression t test does?

Whats the difference between a linear regression t test and goodness of fit test statistic?

Is there such thing as a two proportion chi squared test or is that just an f test?

The only difference between a two proportion t test and a two proportion z test is the knowing of a population standard deviation so that is good.

As you can see I'm all jumbled up.

Are very young infants more likely to imitate actions that are modeled by a person or simulated by an object? This question was the basis of a research study. One action examined was mouth opening. This action was modeled repeatedly by either a person or a doll, and the number of times that the infant imitated the behavior was recorded. Twenty-seven infants participated, with 12 exposed to a human model and 15 exposed to the doll. Summary values are shown below.

	Person Model	Doll Model
x	5.10	3.48
s	1.60	1.30

Is there sufficient evidence to conclude that the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use μ_Person − μ_Doll. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We reject H₀. We do not have convincing evidence that the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll.

We do not reject H₀. We have convincing evidence that the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll.    

We reject H₀. We have convincing evidence that the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll.We do not reject H₀.

We do not have convincing evidence that the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll.