(Hypothetical) In a major national survey of crime victimization, the researchers found that 17.0% of Americans age 12 or older had been a victim of crime. The size of the sample was 6,4,00.

a) Estimate the percentage of Americans age 12 or older who were victims at the 95% confidence level. Write a sentence explaining the meaning of this confidence interval.

b) Estimate the percentage of victims at the 99% confidence level. Write a sentence explaining the meaning of this confidence interval.

Imagine that the Sample size was cut in half to 3,200, but the survey found the same value of 17.0% for the percentage of victims.

c) Would the 95% confidence interval increase or decrease? By how much?

d) Would the 99% confidence interval increase or decrease? By how much?

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

​(a) Determine the 27th percentile for the number of chocolate chips in a bag. ​

(b) Determine the number of chocolate chips in a bag that make up the middle 98​% of bags. ​

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

The effectiveness of antidepressants in treating the eating disorder bulimia was examined in the article “Bulimia Treated with Imipramine: A Placebo-Controlled Double-Blind Study” (American Journal of Psychology [1983]: 554–558). A group of patients diagnosed with bulimia were randomly assigned to one of two treatment groups, one receiving imipramine and the other a placebo. One of the variables recorded was binge frequency. The authors chose to analyze the data using a rank-sum test because it makes no assumption of normality. They stated that “because of the wide range of some measures, such as frequency of binges, the rank sum is more appropriate and somewhat more conservative.” Data on number of binges during one week that are consistent with the findings of the article are given in the following table:

Placebo 8 3 15 3 4 10 6 4

Imipramine 2 1 2 7 3 12 1 5

Do these data strongly suggest that imipramine is effective in reducing the mean number of binges per week? Use a level .05 rank-sum test.

There is one 1$ bill and one 5$ bill in your left pocket and three 1$ bills in your right pocket. You move one bill from the left pocket to the right pocket. After that you take one the remaining bill from the left pocket and one of the bills at random from your right pocket. Let ? denote the amount of money that you take from the left pocket and ? denote the amount of money that you take from the right pocket.

1. ? (?=1, ? =1) is

(a) 1

(b) 3 (correct)

(c) 1

(d) 5

2. ? (?=5, ? =5) is

(a) 0 (correct)

(b) 1/8

(c) 3/8

(d) 1/2

3. ?(? ≥?)is
(a) 1/8

(b) 3/8

(c) 1/2 (correct)

(d) 1

4. Covariance between ? and ? is

(a) 0

(b) −1/2

(c) −1 (correct)

(d) 1

5. Let ? denote the total amount of money that you get from your pockets. V??(?) is

(a) 23/4

(b) 31/8

(c) 19/4

(d) 15/4 (correct)

6. Let ? denote the share of money that you get from the left pocket, i.e. ?/? . Calculate the mean of ?
(a) 1/2

(b) 2/3

(c) 11/13

(d) 5/8 (correct)

An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate A and three slips with votes for candidate B. Suppose these slips are removed from the box one by one. For example, one outcome is BBBAAAA. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.) (a) List all possible outcomes. This answer has not been graded yet. (b) Suppose a running tally is kept as slips are removed. For what outcomes does A remain ahead of B throughout the tally?

consider the following numbers: -5,-3,-1,1,3. assuming that these numbers are the sample data, use a pencil and calculator to calculate the mean, standard deviation and variance. please show work

what is the average age in the class? what is the average feeling? what is the average city?

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable. X for the right tire and Y for the left tire, with joint pdf.

f(x,y) = k(x² + y²), when 20 ≤ x ≤ 30, 20 ≤ y ≤ 30, and

f(x,y) = 0 (otherwise)

A. What is the value of k.

B. what is the probability that both tires are underfilled?

C. What is the marginal distribution of air pressure in the right tire?

Let X be a uniform random variable with pdf f(x) = λe−λx for x > 0, and cumulative distribution function F(x).

(a) Show that F(x) = 1−e −λx for x > 0, and show that this function satisfies the requirements of a cdf (state what these are, and show that they are met). [4 marks]

(b) Draw f(x) and F(x) in separate graphs. Define, and identify F(x) in the graph of f(x), and vice versa. [Hint: write the mathematical relationships, and show graphically what the functions represent.] [4 marks]

(c) X has mgf M(t) = λ(λ−t) −1 . Derive the mean of the random variable from first principles (i.e. using the pdf and the definition of expectation). Also show how this mean can be obtained from the moment generating function. [10 marks]

(d)

(i) Show that F −1 (x) = − 1 λ ln(1 − x) for 0 < x < 1, where ln(x) is the natural logarithm. [4 marks]

(ii) If 0 < p < 1, solve F(xp) = p for xp, and explain what xp represents. [4 marks] (iii) If U ∼ U(0, 1) is a uniform random variable with cdf FU (x) = x (for 0 < x < 1), prove that X = − 1 λ ln(1 − U) is exponential with parameter λ. Hence, describe how observations of X can be simulated. [4 marks]

Suppose men's heights are normally distributed with mean of 176 cm and variance of 25cm^2.

A. What proportion of mean are between 172 cm and 178 cm tall?

B. Find the minimum ceiling of an airplane such that at most 2% of the men walking down the aisle will have to duck their heads.

C. Suppose you take a random sample of 6 men. What is the sampling distribution of the sample mean height? Why?

D. Find the probability that the average height of a random sample of 64 men is greater than 178cm. If these heights were not normally distributed, would you still be able to answer the question? why or why not?

Quantitative studies can be designed in many ways. Please explain the differences between and among the following:

a) experimental, quasi-experimental, and pre-experimental studies (be sure to discuss the concept and usage of a control group)

b) between-subjects and within-subjects studies

c) non and single and double-blind studies

After you differentiate between the above concepts, please upload the pdf of a study and explain how it might be different if one or more of the above were changed.

After you differentiate between the above concepts, please upload the pdf of a study and explain how it might be different if one or more of the above were changed.

upload a pdf study of a similar study to what you have discussed and explained the difference between the pdf and the concepts. you can upload any pdf online that relate to the above.

Listed below are systolic blood pressure measurements​ (in mm​ Hg) obtained from the same woman. Find the regression​ equation, letting the right arm blood pressure be the predictor​ (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05 .

Right Arm 103 102 94 75 75

Left Arm 175 168 149 147 147

The production of wine is a multibillion-dollar world-wide industry. In an attempt to develop a model of wine qual-ity as judged by wine experts, data was collected from red wine variants of Portuguese “Vinho Verde” wine. A sample of 50 wines is stored in VinhoVerde . Develop a multiple linear regression model to predict wine quality, measured on a scale from 0 (very bad) to 10 (excel-lent) based on alcohol content (%) and the amount of chlorides.

State the multiple regression equation. Please use Excel. I cant seem to get it to work with "data analysis"

Problem 3-31 (Algorithmic)

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 2% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 9%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 73000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 12% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 29000, 48000, and 47500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.4 for Boston Components, $2.5 for Able Controls, and $2.8 for Lyshenko Industries.

1. Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.
   
   Let B = number of capacitors ordered from Boston Components
   
   Let A = number of capacitors ordered from Able Controls
   
   Let L = number of capacitors ordered from Lyshenko Industries
   

   Min	B	+	A	+	L
   s.t.
   	B					≤		Boston
   			A			≤		Able
   					L	≤		Lyshenko
   	B ____	+	A____	+	L	=		# useful capacitors
   	B	+	A			≥		Boston - Able %
   					L	≥		Minimum Lyshenko
   B, A, L ≥ 0

   
   Round your answers to the nearest whole number.
   

   Optimal Solution:
   B	____
   A	____
   L	____

2. Suppose that the quality level for reservoir capacitors supplied by Boston Components is much better than estimated. What effect, if any, would this quality level have?
   
   If the quality of reservoir capacitors supplied by Boston Components is much better than expected the optimal solution may change. For example, if Boston Components reduced their defect rate from 9% to 2%, the new optimal solution would increase the number of reservoir capacitors given to Boston Components to .
   
3. Suppose that management is willing to reconsider their requirement that at least 30,000 capacitors must be ordered from Lyshenko Industries. What effect, if any, would this consideration have? If required, round your answer to the nearest cent.
   
   If management removes or reduces the requirement that Lyshenko Industries be ordered at least 30,000 reservoir capacitors the cost will decrease by $__________ per unit decreased.

Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 A.M. to 10:00 P.M. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.60 per hour, but the temp agency managing the part time staff will charge the steakhouse one extra dollar per hour for shifts starting after 3:00 PM. The total number of full-time and part-time employees needed varies with the time of day as shown.

One full-time employee comes on duty at 11:00 A.M., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 P.M. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern.

1. Develop a minimum-cost schedule for part-time employees. What is the total payroll for the part-time employees? If required, round your answer to the nearest dollar.
   
   Total daily salary cost = $  ________
   
   How many part-time shifts are needed?
   ________
   
   Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts.
2. Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. If your answer is zero, enter "0".
   
   Optimal schedule for part-time employees:
   

   Starting Time	Number of part- time employees (4-hour shifts)	Number of part- time employees (3-hour shifts)
   11:00 A.M.	________	________
   12:00 P.M.	________	________
   1:00 P.M.	________	________
   2:00 P.M.	________	________
   3:00 P.M.	________	________
   4:00 P.M.	________	________
   5:00 P.M.	________	________
   6:00 P.M.	________	________
   7:00 P.M.	________	________

   
   How many part-time shifts are needed?
   ________
   
   
   What is the cost savings compared to the previous schedule? If required, round your answer to the nearest cent.
   
   Total cost reduced to $ ________.