1. A study was conducted of recent high school graduates who began full-time jobs rather than going to college. We wish to find the average starting income µ of such workers. A random sample of size 60 gave a sample mean of $24,500 with a population standard deviation of $2350.Round answers to 2 decimal places.

1. Find the standard error.

2. Identify the upper and lower z score for a 95% confidence interval for µ.

3. Calculate the upper and lower bounds of the confidence interval.

Answer following:

1. After several studies, professor smith concludes that there is a zero correlation between body weight and bad tempers. This means that

2. A traffic safety officer conducted an experiment to determine whether there is a correlation between people's ages and driving were randomly sampled and the following data were collected.

Age: 20 25 45 46 60 65

Speed: 60 47 55 38 45 35

The value of pearson r equals

3. If sy=1, and sx=1, and r=0.6, what will the value of b be?

4. Correlation is the same thing as causation = t/f

5. A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent of body fat following scores were recorded.

Exercise (minutes): 10 18 26 33 44

% Body Fat: 30 25 18 17 14

Assuming the linear relationship holds, the least square regression line for predicting % body fat from the amount of exercise ___

6. What is the probability of rolling two sixes with one roll of a pair of dice ( a six and a six)? =

7. In a positive relationship, =

8. If the regression equation for a data set is Y'=2.650X+11.250, then the value of Y' for X=33 is =

9. Suppose you are going to randomly order individuals A,B,C,D,E, and F. the probability that the first person will be A and the second person will be B is =

10. The probability of drawing an ace followed by a king (without replacement) equals =

Suppose systolic blood pressure of 17-year-old females is approximately normally distributed with a mean of 113 mmHg and a standard deviation of 24.71 mmHg. If a random sample of 22 girls were selected from the population, find the following probabilities:

a) The mean systolic blood pressure will be below 109 mmHg. probability =

b) The mean systolic blood pressure will be above 118 mmHg. probability =

c) The mean systolic blood pressure will be between 106 and 125 mmHg. probability =

d) The mean systolic blood pressure will be between 106 and 113 mmHg. probability =

For each of the following questions, determine which kind of prediction confidence interval is appropriate.

a). Predict the humidity level in this greenhouse tomorrow when we set the temperature level at 31 °C?

b). Predict how much do families spend, on the average, on meals? Suppose the family income is $50,000

c). Predict how many kilowatt-hours of electricity will be consumed in September by commercial and industrial users in the Twin Cities service area, given that the index of business activity for area remains at the level of August?

d). Predict how many kilowatt-hours of electricity will be consumed daily on average in September (30 days) by commercial and industrial users in the Twin Cities service area, given that the index of business activity for area remains at the level of August 31?

a. Why is a random sample typically not collected? Develop a research question and determine how we would need to organize the study to use random sampling.

b. Imagine that you flip a coin 50 times. How would you use the terms trial, outcome, and success to describe this task?

c. What is the difference between the null hypothesis and the research, or alternative, hypothesis? Why do we never accept the null hypothesis or the research hypothesis?

d. What are Type I and Type II errors, and why are Type I errors considered to be particularly detrimental to research?

Answer true or false with a sentence or two explanation.

1. In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

2. A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

3. The larger the confidence level used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

4. The term 1 – alpha refers to the probability that a confidence interval does not contain the population parameter.

5. In the formula , Xbar plus or minus z alpha / 2 times the stand dev. / sq root of n. the subscript alpha over 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

6. When constructing confidence interval for a parameter, we generally set the confidence level 1 - alpha close to 1 (usually between 0.90 and 0.99) because it is the probability that the interval includes the actual value of the population parameter.

7. Suppose that a 90% confidence interval for Mu is given by Xbar plus or minus .75. This notation means that we are 90% confident that Mu falls between xbar minus .75 and xbar plus .75

8. When a sample standard deviation is used to estimate a population standard deviation, the margin of error is computed by using the standard normal distribution.

9. The width of a confidence interval is independent of the sample size.

10. Suppose a sample size of 5 has mean 9.60. If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

Problem 1. When Abe graduated from Texas A&M, he bought a diamond ring with a golden insignia to impress his high school friends. The person most impressed was his old sweetheart, Beth. They grew so fond of each other that Abe asked Beth to wear his ring. Then the quarreling began. The relationship deteriorated until, in a fit of anger, Beth enrolled as a student at University of Texas. Abe, naturally, broke off the relationship and asked for the return of his ring. Beth replied that it was a gift to her and she was not about to return it. He answered that he had only loaned it to her to wear for the duration of their friendship. Abe and Beth are now involved in a legal dispute over the ring. Beth possesses the ring and she declares that she intends to sell it. Abe threatens to sue her. If Abe wins at trial, the court will require Beth to return the ring to him. The ring is worth $1,000 to Abe. If Beth wins at trial, the court will allow her to keep the ring. She would then sell the ring for $600 to an acquaintance. (The acquaintance does not know Abe and will not resell the ring to him.) In the event of a trial, each one expects to win with probability 0.5. A trial will cost Abe $250 and it will also cost Beth $250. Abe and Beth start negotiating to reach a settlement and avoid a trial. The costs of settling out of court are nil. Assume that these numbers are common knowledge for all parties.

Abe's expected value from going to trial is:

Beth's expected value from going to trial is:

The bargaining surplus over which the two are negotiating is:

If Abe and Beth were to split the bargaining surplus evenly, what kind of exchange (ring and currency) should take place?

A) Abe should let Beth keep the ring in exchange of her giving him $200.

B) Beth should give Abe the ring in exchange of him giving her $600.

C) Beth should give Abe the ring in exchange of him giving her $400.

D) Beth should give Abe the ring in exchange of him giving her $250.

E) Abe should let Beth keep the ring in exchange of her giving him $1000.

1. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F. What is the probability (4 significant figures) that a daily temperature would be 72 degrees F or less? Would this be considered unusual, or not unusual?

2. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F. What is the probability that a daily temperature would be between 90 and 100 degrees F? Would such temperatures be considered unusual, or not unusual?

3. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F. What is the 90th percentile for all such daily temperatures? Round to the nearest hundredth of a degree; don't forget units of measure

4. The daily temperature in August in a region is normally distributed with a mean of 86 degrees F and a standard deviation of 4 degrees F. What is the centered, symmetric interval containing 80% of all such temperatures? (round to the nearest hundredth of a degree); don't forget units of measure

A marketing company based out of New York City is doing well and is looking to expand internationally. The CEO and VP of Operations decide to enlist the help of a consulting firm that you work for, to help collect data and analyze market trends.

You work for Mercer Human Resources. The Mercer Human Resource Consulting website (www.mercer.com) lists prices of certain items in selected cities around the world. They also report an overall cost-of-living index for each city compared to the costs of hundreds of items in New York City (NYC). For example, London at 88.33 is 11.67% less expensive than NYC.

More specifically, if you choose to explore the website further you will find a lot of fun and interesting data. You can explore the website more on your own after the course concludes.

https://mobilityexchange.mercer.com/Insights/cost-of-living-rankings#rankings

In the Excel document, you will find the 2018 data for 17 cities in the data set Cost of Living. Included are the 2018 cost of living index, cost of a 3-bedroom apartment (per month), price of monthly transportation pass, price of a mid-range bottle of wine, price of a loaf of bread (1 lb.), the price of a gallon of milk and price for a 12 oz. cup of black coffee. All prices are in U.S. dollars.

You use this information to run a Multiple Linear Regression to predict Cost of living, along with calculating various descriptive statistics. This is given in the Excel output (that is, the MLR has already been calculated. Your task is to interpret the data). Based on this information, in which city should you open a second office in? You must justify your answer. If you want to recommend 2 or 3 different cities and rank them based on the data and your findings, this is fine as well. This should be ¾ to 1 page, no more than 1 single-spaced page in length, using 12-point Times New Roman font. You do not need to do any calculations, but you do need to pick a city to open a second location at and justify your answer based upon the provided results of the Multiple Linear Regression. Think of this assignment as the first page of a much longer report, known as an Executive Summary, that essentially summarizes your findings briefly and at a high level. This needs to be written up neatly and professionally. This would be something you would present at a board meeting in a corporate environment.

City Cost of Living Index Rent (in City Centre) Monthly Pubic Trans Pass Loaf of Bread Milk Bottle of Wine (mid-range) Coffee

Mumbai 31.74 $1,642.68 $7.66 $0.41 $2.93 $10.73 $1.63

Prague 50.95 $1,240.48 $25.01 $0.92 $3.14 $5.46 $2.17

Warsaw 45.45 $1,060.06 $30.09 $0.69 $2.68 $6.84 $1.98

Athens 63.06 $569.12 $35.31 $0.80 $5.35 $8.24 $2.88

Rome 78.19 $2,354.10 $41.20 $1.38 $6.82 $7.06 $1.51

Seoul 83.45 $2,370.81 $50.53 $2.44 $7.90 $17.57 $1.79

Brussels 82.2 $1,734.75 $57.68 $1.66 $4.17 $8.24 $1.51

Madrid 66.75 $1,795.10 $64.27 $1.04 $3.63 $5.89 $1.58

Vancouver 74.06 $2,937.27 $74.28 $2.28 $7.12 $14.38 $1.47

Paris 89.94 $2,701.61 $85.92 $1.56 $4.68 $8.24 $1.51

Tokyo 92.94 $2,197.03 $88.77 $1.77 $6.46 $17.75 $1.49

Berlin 71.65 $1,695.77 $95.34 $1.24 $3.52 $5.89 $1.71

Amsterdam 85.9 $2,823.28 $105.93 $1.33 $4.34 $7.06 $1.71

New York 100 $5,877.45 $121.00 $2.93 $3.98 $15.00 $0.84

Sydney 90.78 $3,777.72 $124.55 $1.94 $4.43 $14.01 $2.26

Dublin 87.93 $3,025.83 $144.78 $1.37 $4.31 $14.12 $2.06

London 88.33 $4,069.99 $173.81 $1.23 $4.63 $10.53 $1.90

mean 75.49 $2,463.12 $78.01 $1.47 $4.71 $10.41 $1.76

median 82.2 $2,354.10 $74.28 $1.37 $4.34 $8.24 $1.71

min 31.74 $569.12 $7.66 $0.41 $2.68 $5.46 $0.84

max 100 $5,877.45 $173.81 $2.93 $7.90 $17.75 $2.88

Q1 66.75 $1,695.77 $41.20 $1.04 $3.63 $7.06 $1.51

Q3 88.33 $2,937.27 $105.93 $1.77 $5.35 $14.12 $1.98

New York 100 $5,877.45 $121.00 $2.93 $3.98 $15.00 $0.84

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.935824078

R Square 0.875766706

Adjusted R Square 80.12%

Standard Error 8.30945321

Observations 17

ANOVA

df SS MS F Significance F

Regression 6 4867.380768 811.2301279 11.74895331 0.00049963

Residual 10 690.4701265 69.04701265

Total 16 5557.850894

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept  35.63950178 15.41876933 2.311436213 0.043401141 1.284342794 69.99466077 1.284342794 69.99466077

Rent (in City Centre) -0.003212852 0.003974813 -0.808302603 0.437722785 -0.012069287 0.005643584 -0.012069287 0.005643584

Monthly Pubic Trans Pass 0.299650003 0.076964051 3.89337619 0.002993072 0.128163411 0.471136595 0.128163411 0.471136595

Loaf of Bread 16.59481787 6.713301249 2.47193106 0.032995588 1.636650533 31.55298521 1.636650533 31.55298521

Milk 2.912081706 1.98941146 1.463790555 0.173964311 -1.520603261 7.344766672 -1.520603261 7.344766672

Bottle of Wine (mid-range) -0.889805486 0.740190296 -1.202130709 0.257006081 -2.539052244 0.759441271 -2.539052244 0.759441271

Coffee -2.527438053 6.484555358 -0.389762738 0.704884259 -16.97592778 11.92105168 -16.97592778 11.92105168

RESIDUAL OUTPUT

Observation Predicted Cost of Living Index Residuals Standard Residuals City

1 34.32607137 -2.586071368 -0.39366613 Mumbai

2 53.21656053 -2.266560525 -0.345028417 Prague

3 49.41436121 -3.964361215 -0.603477056 Warsaw

4 58.63611785 4.42388215 0.673427882 Athens

5 73.08449538 5.105504624 0.777188237 Rome

6 86.50256003 -3.052560026 -0.464677621 Seoul

7 75.89216916 6.307830843 0.960213003 Brussels

8 67.7257781 -0.975778105 -0.148538356 Madrid

9 90.51996071 -16.45996071 -2.50562653 Vancouver

10 81.07358731 8.866412685 1.349694525 Paris

11 83.80564633 9.134353675 1.390481989 Tokyo

12 80.02510391 -8.37510391 -1.274904778 Berlin

13 82.41624318 3.483756815 0.530316788 Amsterdam

14 97.75654811 2.243451893 0.341510693 New York

15 87.73993924 3.040060757 0.462774913 Sydney

16 86.81668291 1.11331709 0.169475303 Dublin

17 94.36817468 -6.038174677 -0.919164446 London

Can someone explain a,b and c? The answers are correct I believe but I just need a more clear explenation on the formulas and final answers

If 2 cards are drawn from a well-shuffled deck of 52 playing cards, what are the probabilities of getting

Answer:

Total no of ways of drawing 2 cards from a well-shuffled deck of 52 playing cards = ⁵²C₂ = 1326

(a)        two spades;

Number of ways getting 2 spades / total number of ways = (¹³C₂)/1326 = 78/1326 = 0.0588

(b)        two aces;

Number of ways getting 2 aces / total number of ways = (⁴C₂)/1326 = 4/1326 = 0.003

(c)        a king and a queen?

            13*13/1326 = 0.12745

A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. We will assume that based on extensive previous research, it is known that in the general population the number of such dreams per month follows a normal curve, with μ= Unknown node type: span and σ=4 . The researcher wants to test the prediction that the number of such dreams will be greater among people who have recently experienced a traumatic event. Thus, the psychologist studies 36 individuals who have recently experienced a traumatic event, having them keep a record of their dreams for a month. Their mean number of alone dreams is 8. Should you conclude that people who have recently had a traumatic experience have a significantly different number of dreams in which they are alone? (a) Carry out a Z test using the five steps of hypothesis testing (use the .05 level). (b) Make a drawing of the distributions involved. (c) Explain your answer to a person who has never had a course in statistics. (d) ADVANCED TOPIC: Figure the 95% confidence interval.

1. The association between the variables "dollars earned" and "hours worked" for a worker at store would be

QUESTION 2

The association between the variables "GPA" and "hours spent studying" for a student would usually be

QUESTION 3

The association between the variables "cost of a book" and "the buyers body temperature" would be

QUESTION 4

The association between the variables "airfare" and "distance to destination" would be

QUESTION 5

A graph that will help to one to see what type of curve might best fit the bivariate data

QUESTION 6

If the correlation coefficient for a linear regression is -0.932. there is sufficient evidence that a linear relationship exists between the x and y data

QUESTION 7

Which of the following correlation coefficients represents the most linear function?

QUESTION 8

If the correlation coefficient for linear regression is 0.25. there is sufficient evidence that a linear relationship exists between the x and y data

QUESTION 9

A data point that lies statistically far from the regression line is a potential

QUESTION 10

1. correlation5:
   
   If the correlation coefficient is 0.90, the value of the coefficient of determination would be

QUESTION 11

Use your TI83 to determine the correlation coefficient of the following set of points. Round correctly to the nearest hundredth.

(4, 4), (-2, -7), (3, 3), (4, -1)

QUESTION 12

Use your TI83 to determine the correlation coefficient of the following set of points. Round correctly to the nearest hundredth.

(4, 4), (-2, -4), (7, -2), (4, 1)

QUESTION 13

Use your TI83 to determine the correlation coefficient of the following set of points. Round correctly to the nearest hundredth.

(2, 4), (1, -1), (2, 2), (5, -4)

As a part of a new healthcare reform, hospitals must report incidence of specific demographic and health care outcomes to maintain funding. Within this report, it was found that 23.3% the Medicare population in Westmoreland county is Diabetic. As part of a random survey to determine if current preventative measures are helping to target this, a random sample of 50 individuals within the Medicare population we sampled.

Let X be the number of individuals who are Diabetic.

1. Can X be considered a binomially distributed random variable? Why?

2. Identify n and p for this problem.

3. Can variables X be well-approximated by normal random variables?

4. What is the expected number of diabetic individuals for this problem?

5. What is the variance for the number of diabetic individuals for this problem?

6. How many combinations are possible that consists of exactly 20 people that are diabetic?

7. What is the probability of observing 20 diabetic individuals?

Describe how simple linear regression analysis and multiple regression are used to support areas of industry research, academic research, and scientific research.

1. A sample of eight resistors of a certain type resulted as follows:

                  43, 46, 42, 38, 40, 46, 49, 40

Compute the following:

1. Sample Mean
2. Sample Variance
3. Sample Median
4. 25% Percentile
5. 75% Percentile

2. Consider the following pdf:

      P(X = 0) = 0.48, P(X = 1) = 0.39, P(X = 2) = 0.12, and P(X = 3) = 0.01.

Find the following:

• Do the plot for P(X) and F(X)
• F(0) = P(X ≤ 0) =
• F(1) = P(X ≤ 1) =
• F(2) = P(X ≤ 2) =
• F(3) = P(X ≤ 3) =
• P(1 ≤ X ≤ 2) =
• μ_x =
• σ_x² =