1. A store sells three different clothing designs and has recorded sales of each over five different 24-hour periods:

Design A         Design B         Design C

     16                    33                    23

     18                    31                    27

     19                    37                    21

     17                    29                    28

     13                    34                    25

Use the Kruskal-Wallis H test and the Chi-Square table at the 0.05 level to compare the three designs.

Use the data consisting of IQ score and brain volume

​(cm cubedcm3​).

Find the best predicted IQ score for someone with a brain volume of 1003 cm cubed. Use a significance level of 0.05.

Brain Volume   IQ score

900 85

1275 102

936 102

1444 98

1473 112

1263 129

1090 93

1218 89

1324 89

1364 82

942 97

1490 129

1339 82

1159 85

1087 92

964 127

1138 113

1058 93

1365 96

1081 115

The regression equation is? ( round the x- coefficient five decimal places as needed. round the constant to two decimal places as needed.)

The heights of a female population follow a normal distribution with a mean of 48 inches and a standard deviation of 6 inches. If a random sample of 16 subjects were taken, what is the probability that the average height of the sample is higher than 50 inches?

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

8585

mm Hg. Use a significance level of

0.050.05.

Right Arm	100	99	92	79	80
Left Arm	176	170	145	144	146

n	alphaαequals=0.05	alphaαequals=0.01	​NOTE: To test Upper H 0H0​: rhoρequals=0 against Upper H 1H1​: rhoρnot equals≠​0, reject Upper H 0H0 if the absolute value of r is greater than the critical value in the table.
4	0.950	0.990
5	0.878	0.959
6	0.811	0.917
7	0.754	0.875
8	0.707	0.834
9	0.666	0.798
10	0.632	0.765
11	0.602	0.735
12	0.576	0.708
13	0.553	0.684
14	0.532	0.661
15	0.514	0.641
16	0.497	0.623
17	0.482	0.606
18	0.468	0.590
19	0.456	0.575
20	0.444	0.561
25	0.396	0.505
30	0.361	0.463
35	0.335	0.430
40	0.312	0.402
45	0.294	0.378
50	0.279	0.361
60	0.254	0.330
70	0.236	0.305
80	0.220	0.286
90	0.207	0.269
100	0.196	0.256

PrintDone

What is the regression equation?

The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of

3939

inches. Is the result close to the actual weight of

126126

​pounds? Use a significance level of 0.05.

Chest size​ (inches)	44	41	41	55	51	42
Weight​ (pounds)	213	206	176	309	300	178

n	alphaαequals=0.05	alphaαequals=0.01	​NOTE: To test H0​: rhoρequals=0 against H1​: rhoρnot equals≠​0, reject H0 if the absolute value of r is greater than the critical value in the table.
4	0.950	0.990
5	0.878	0.959
6	0.811	0.917
7	0.754	0.875
8	0.707	0.834
9	0.666	0.798
10	0.632	0.765
11	0.602	0.735
12	0.576	0.708
13	0.553	0.684
14	0.532	0.661
15	0.514	0.641
16	0.497	0.623
17	0.482	0.606
18	0.468	0.590
19	0.456	0.575
20	0.444	0.561
25	0.396	0.505
30	0.361	0.463
35	0.335	0.430
40	0.312	0.402
45	0.294	0.378
50	0.279	0.361
60	0.254	0.330
70	0.236	0.305
80	0.220	0.286
90	0.207	0.269
100	0.196	0.256
n	alphaαequals=0.05	alphaαequals=0.01

PrintDone

What is the regression equation?

A survey of the members of a large professional engineering society is conducted to determine their views on proposed

changes to an ASTM measurement standard. Overall 80% of the entire membership favor the proposed changes.

(a) If possible, describe the center, dispersion, and shape of the sampling distribution of the proportion of engineers for

samples of size 20 who favor the proposed changes. Explain your answer including which of these three aspects of

distribution you can & cannot describe and why.

(b) If possible, describe the center, dispersion, and shape of the sampling distribution of the proportion of engineers for

samples of size 50 who favor the proposed changes. Explain your answer including which of these three aspects of

distribution you can & cannot describe and why.

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.

x	88	99	66	1212	1515	1313	1111	1010	77	55	1414
y	15.0915.09	16.9816.98	10.3110.31	20.6920.69	21.4321.43	21.2721.27	19.7819.78	18.5518.55	12.8712.87	7.437.43	21.5121.51

y(^ above the y)=?+?. Round to two decimals as needed.

Write the following linear program in standard form. If your answer is zero, enter “0”. If the constant is "1" it must be entered in the box.

Max	12A	+	6B
s.t.
	A	−	2B	≤	420
	6A	+	8B	≤	1,300
	10A	−	2B	≤	250
A, B ≥ 0

	A	+	B	+	S1	+	S2	+	S3
s.t.
	A	−	B	+	S1
	A	+	B			+	S2
	A	−	B					+	S3
									A, B, S1, S2, S3

In a certain county, the sizes of family farms approximately follow mound-shaped (normal) distribution with a mean of 472 acres and a standard deviation of 27 acres.

(a) According to the empirical rule, approximately __% of family farms have a size between 418 and 526 acres.

(b) According to the empirical rule, approximately __% of family farms have a size between 391 and 553 acres.

(c) According to the empirical rule, approximately __% of family farms have a size between 445 and 499 acres.

For homes in a certain state, electric consumption amounts last year approximately followed a mound-shaped (normal) distribution with a mean of 1034 kilowatt-hours and a standard deviation of 182 kilowatt-hours.

(a) According to the empirical rule, approximately 99.7% of values in the distribution will be between these two bounds:
Lower-bound =___ kilowatt-hours and upper-bound = ___ kilowatt-hours.

(b) According to the empirical rule, approximately 68% of values in the distribution will be between these two bounds:
Lower-bound = ___ kilowatt-hours and upper-bound = ___ kilowatt-hours.

(c) According to the empirical rule, approximately 95% of values in the distribution will be between these two bounds:
Lower-bound = ___ kilowatt-hours and upper-bound = ___kilowatt-hours.

Aminah wish to perform the hypothesis testing H0: μ =1 versus H1: μ <1 versus with α=0.10. . The sample size 25 was obtained independently from a population with standard deviation 10. State the distribution of the sample mean given that null hypothesis is true and find the critical value, then calculate the values of sample mean if she reject the null hypothesis. Finally, compute the p-value, if the sample mean is -2.

The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones industrial Average is based on 30 large companies. The data giving the annual percentage returns for each of these stock indexes for 25 years are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Year	DJIA % Return	Russell 1000 % Return
1988	8.82	12.33
1989	26.59	26.44
1990	-3.68	-4.57
1991	16.04	28.88
1992	5.38	1.66
1993	18.58	7.69
1994	6.29	1.76
1995	30.62	37.10
1996	21.49	17.49
1997	19.04	28.68
1998	12.83	29.46
1999	29.15	15.89
2000	-3.01	-6.42
2001	-9.85	-13.16
2002	-15.56	-25.79
2003	27.78	29.69
2004	7.71	10.82
2005	-4.84	8.73
2006	13.34	13.72
2007	8.12	7.04
2008	-31.04	-42.92
2009	20.72	22.47
2010	8.76	9.59
2011	2.80	-3.13
2012	8.40	11.02

a. Which of the following scatter diagrams accurately represents the data set?

#1	Russell 1000 DJIA	#2	Russell 1000 DJIA
#3	Russell 1000 DJIA	#4	Russell 1000 DJIA

_________Scatter diagram #1Scatter diagram #2Scatter diagram #3Scatter diagram #4

b. Compute the sample mean and standard deviation for each index (to 2 decimals).

	sample mean	standard deviation
DJIA:
Russell 1000:

c. Compute the sample correlation coefficient for these data (to 3 decimals).

d. Discuss similarities and differences in these two indexes.

_________There is a strong positive linear association between DJIA and Russell 1000There is a moderate positive linear association between DJIA and Russell 1000There is neither a positive nor a negative linear association between DJIA and Russell 1000There is a moderate negative linear association between DJIA and Russell 1000There is a strong negative linear association between DJIA and Russell 1000

The variance of the Russell 1000 is slightly _________largersmaller than that of the DJIA.

a. Which of the following scatter diagrams accurately represents the data set?

#1	Russell 1000 DJIA	#2	Russell 1000 DJIA
#3	Russell 1000 DJIA	#4	Russell 1000 DJIA

_________Scatter diagram #1Scatter diagram #2Scatter diagram #3Scatter diagram #4

b. Compute the sample mean and standard deviation for each index (to 2 decimals).

	sample mean	standard deviation
DJIA:
Russell 1000:

c. Compute the sample correlation coefficient for these data (to 3 decimals).

d. Discuss similarities and differences in these two indexes.

_________There is a strong positive linear association between DJIA and Russell 1000There is a moderate positive linear association between DJIA and Russell 1000There is neither a positive nor a negative linear association between DJIA and Russell 1000There is a moderate negative linear association between DJIA and Russell 1000There is a strong negative linear association between DJIA and Russell 1000

The variance of the Russell 1000 is slightly _________largersmaller than that of the DJIA.

You believe that there is a difference in salaries between genders in your industry. You know that the average salary for males is $100,000 per year, but you cannot find any information on female salaries. Thus, you collect data on female salaries to test your belief. For your study, what would be your null hypothesis?

A. µ < 100,000

B. µ = 100,000

C. µ ≤ 100,000

D. not enough information

This problem is from 2008.

The US Open is an annual two week tennis event in Flushing NY in late August, early September.

In a year with no significant rain interruption, the US Open makes approximately $275 million in revenue and incurs expenses of approximately $225 million, for a profit of $50 million. Of the $275 million in revenue approximately $100 million is from ticket sales. As a non-profit organization, it incurs no tax.

The US Open can work around rain delays but if all play is suspended in either the afternoon or evening sessions, tickets are good for the same session in the following year, in which case the USTA foregoes revenue. The largest ticket prices are for the women’s and men’s finals so a rain-out on either of these days forgoes the most revenue.

The Open is interested in buying a contract to protect itself from foregone revenues from rain interruptions during the finals. Working with its insurance broker, it approaches the insurance market to see if it can buy a weather derivative or insurance policy.

The US Open estimates that between foregone ticket sales and lost margin on concessions and broadcasting rights, a rain out on either the men’s or women’s finals will mean $30 mil in lost profits.

The insurance broker is able to secure an insurance policy that will indemnify the US Open if rainfall occurs during the men’s or women’s finals. The policy treats each event separately, meaning there is coverage and a corresponding premium charged for postponement of either final. The insurer is willing to provide a policy covering each separate event that will indemnify the US Open with a limit of $30 million and a policy premium of $10 million for each. As with all insurance policies, the US Open can collect the insurance payments only once it demonstrates the losses.

The weather desks at three major reinsurance holding companies with broker/dealers supply the probabilities associated with significant rainfall (> ¼ inch) on days 13 and 14 of this calendar year, which is 20% for either day, and conditional on rain on the 13th day, the chance of rain on the 14th day is 30%.

Write out all possible rain/dry possibilities for the 13th and 14th days, with their associated probabilities.

Without insurance, what are the profits if there are rain postponements to either or both finals?

Without insurance, what are the expected profits?

With insurance, what are profits if there are rain postponements?

With insurance what are profits if there is no rain?

What are the expected profits if insurance is purchased?

Should the US Open explore including additional days into the policy?

Over a ten year period, assuming baseline revenue and costs are approximately the same amounts as today, what would the US Open expect to earn (i) in the absence of an insurance policy and (ii) with the insurance policy?

The weather desk is also willing to write two weather derivative contracts, one for day 13 and one for day 14, each with a payout of $30 million and a cost of $12 million. The derivative pays the US Open regardless of whether play is suspended or not. It pays based on measured rainfall within 24 hour period exceeding ¼ of an inch.

What is the best strategy for the US Open to manage its exposure to rain?

Explain.

Without insurance, what are the profits if there are rain postponements to either or both finals?

Without insurance, what are Expected profits?

With insurance, what are profits if there are rain postponements?

With insurance what are profits if there is no rain?

Should the US Open explore including additional days into the policy?

Over a ten year period, assuming baseline revenue and costs are approximately the same amounts as today, what would the US Open expect to earn (i) in the absence of an insurance policy and (ii) with the insurance policy?

What is the best strategy for the US Open to manage its exposure to rain?

This problem is from 2008.

The US Open is an annual two week tennis event in Flushing NY in late August, early September.

In a year with no significant rain interruption, the US Open makes approximately $275 million in revenue and incurs expenses of approximately $225 million, for a profit of $50 million. Of the $275 million in revenue approximately $100 million is from ticket sales. As a non-profit organization, it incurs no tax.

The US Open can work around rain delays but if all play is suspended in either the afternoon or evening sessions, tickets are good for the same session in the following year, in which case the USTA foregoes revenue. The largest ticket prices are for the women’s and men’s finals so a rain-out on either of these days forgoes the most revenue.

The Open is interested in buying a contract to protect itself from foregone revenues from rain interruptions during the finals. Working with its insurance broker, it approaches the insurance market to see if it can buy a weather derivative or insurance policy.

The US Open estimates that between foregone ticket sales and lost margin on concessions and broadcasting rights, a rain out on either the men’s or women’s finals will mean $30 mil in lost profits.

The insurance broker is able to secure an insurance policy that will indemnify the US Open if rainfall occurs during the men’s or women’s finals. The policy treats each event separately, meaning there is coverage and a corresponding premium charged for postponement of either final. The insurer is willing to provide a policy covering each separate event that will indemnify the US Open with a limit of $30 million and a policy premium of $10 million for each. As with all insurance policies, the US Open can collect the insurance payments only once it demonstrates the losses.

The weather desks at three major reinsurance holding companies with broker/dealers supply the probabilities associated with significant rainfall (> ¼ inch) on days 13 and 14 of this calendar year, which is 20% for either day, and conditional on rain on the 13^th day, the chance of rain on the 14^th day is 30%.

1. Write out all possible rain/dry possibilities for the 13^th and 14^th days, with their associated probabilities.
2. Without insurance, what are the profits if there are rain postponements to either or both finals?
3. Without insurance, what are the expected profits?
4. With insurance, what are profits if there are rain postponements?
5. With insurance what are profits if there is no rain?
6. What are the expected profits if insurance is purchased?
7. Should the US Open explore including additional days into the policy?
8. Over a ten year period, assuming baseline revenue and costs are approximately the same amounts as today, what would the US Open expect to earn (i) in the absence of an insurance policy and (ii) with the insurance policy?

The weather desk is also willing to write two weather derivative contracts, one for day 13 and one for day 14, each with a payout of $30 million and a cost of $12 million. The derivative pays the US Open regardless of whether play is suspended or not. It pays based on measured rainfall within 24 hour period exceeding ¼ of an inch.

1. What is the best strategy for the US Open to manage its exposure to rain?

Explain.

1. Without insurance, what are the profits if there are rain postponements to either or both finals?
2. Without insurance, what are Expected profits?

3. With insurance, what are profits if there are rain postponements?
4. With insurance what are profits if there is no rain?

5. Should the US Open explore including additional days into the policy?

6. Over a ten year period, assuming baseline revenue and costs are approximately the same amounts as today, what would the US Open expect to earn (i) in the absence of an insurance policy and (ii) with the insurance policy?
7. What is the best strategy for the US Open to manage its exposure to rain?

please make sure the second part is answer.  

Two hospital emergency rooms use different procedures for triage of their patients. A local health care provider conducted a study to determine if there is a significant difference in the mean waiting time of patients for both hospitals. The 40 randomly selected subjects from Medina General Hospital (population 1) produce a mean waiting time of 18.3 minutes and a standard deviation of 2.1 minutes. The 50 randomly selected patients from Southwest General Hospital (population 2) produce a mean waiting time of 19.2 minutes and a standard deviation of 2.92 minutes. Using a significance level of α = .02, the critical value(s) for rejecting the null hypothesis is(are) -2.33 ±1.988 +2.33 -2.37 ±2.33 +2.37 ±2.37 +1.988 -1.988