The following data are from a completely randomized design.

1. Compute the sum of squares between treatments. Round the intermediate calculations to whole number.
     
   
2. Compute the mean square between treatments.
     
   
3. Compute the sum of squares due to error.
     
   
4. Compute the mean square due to error (to 1 decimal).
     
   
5. Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole number. Round all Mean Squares to one decimal place. Round F to two decimal places. Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Treatments
   Error
   Total

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other.

Losses $                                                          Probability of Loss

$10,000                                                           0.20

$20,000                                                           0.10

$50,000                                                           0.06

$100,000                                                         0.03

$500,000                                                         0.01

Now suppose Terry joins a risk sharing arrangement with other small business owners and now a total of 18 buildings are in the risk sharing pool. Assume that the property losses for the additional buildings follow the same probability distribution as that given for Terry’s buildings and losses are independent.

a. Find the average or expected loss of this larger group of buildings in a given year.

b. Calculate the standard deviation of the distribution.

c. Find the Coefficient of Variation

d. What happens to variance or risk for Terry after the sharing arrangement is in place?

e. What would you expect to happen to variance or risk if the pool was extremely large? Why?

f. What is Terry’s actuarially fair premium now? What has happened to his risk premium now?

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags. A 23 bag sample had a mean of 423 grams with a standard deviation of 14. Assume the population is normally distributed. A level of significance of 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.

(a)Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

State the null and alternative hypotheses.

H₀: The type of ticket purchased is not independent of the type of flight.
H_a: The type of ticket purchased is independent of the type of flight.H₀: The type of ticket purchased is not mutually exclusive from the type of flight.
H_a: The type of ticket purchased is mutually exclusive from the type of flight.    H₀: The type of ticket purchased is independent of the type of flight.
H_a: The type of ticket purchased is not independent of the type of flight.H₀: The type of ticket purchased is mutually exclusive from the type of flight.
H_a: The type of ticket purchased is not mutually exclusive from the type of flight.

Find the value of the test statistic. (Round your answer to three decimal places.)

Please explain how to get test statistic on excel and by hand.

Find the p-value. (Round your answer to four decimal places.)

Please explain how to get test statistic on excel or by hand.

p-value =

State your conclusion.

Reject H₀. We conclude that the type of ticket purchased is independent of the type of flight.

Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are independent.    

Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are not independent.

Reject H₀. We conclude that the the type of ticket purchased is not independent of the type of flight.

(b)

Discuss any dependence that exists between the type of ticket and type of flight.

The type of ticket purchased is independent of the type of flight.

A higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights. Economy class tickets are purchased more for domestic flights.    

A higher percentage of first class and business class tickets are purchased for domestic flights compared to international flights. Economy class tickets are purchased more for international flights.

A lower percentage of economy class tickets are purchased for domestic flights compared to international flights. First class and business class tickets are purchased more for domestic flights.

A magazine provided overall customer satisfaction scores for AT&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 was used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. The ratings for the four cell-phone services in 20 metropolitan areas are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

a. Consider T-Mobile first. What is the median rating (to 1 decimal)?

b. Develop a five-number summary for the T-Mobile service.

c. Are there outliers for T-Mobile?

_________Yes, the data contain outliersNo, the data do not contain outliers

d. Repeat parts (b) and (c) for the other three cell-phone services.

Are there outliers for AT&T?

_________Yes, the data contain outliersNo, the data do not contain outliers

Are there outliers for Sprint?

_________Yes, the data contain outliersNo, the data do not contain outliers

Are there outliers for Verizon?

_________Yes, the data contain outliersNo, the data do not contain outliers

e. Which of the following box plots accurately displays the data set?

_________Box plot #1Box plot #2Box plot #3Box plot #4

Which service did the magazine recommend as being best in terms of overall customer satisfaction?

_________AT&TSprintT-MobileVerizon

A psychologist hypothesizes that depression decreases with aging. It is known that the general population scores a 41 on a standardized depression test where a higher score indicates more depression. The psychologist obtains a sample of individuals that are all over 65 years old. What can the psychologist conclude with an α of 0.05? The data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- elderly standardized depression test general population depression aging
Sample:
---Select--- elderly standardized depression test general population depression aging

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The elderly are significantly more depressed than the population.

The elderly are significantly less depressed than the population.    

The elderly did not significantly differ on depression than the population.

what is the difference between mutually exclusive, independent and conditional probabilities?

Part 1. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $2.99 to $3.99. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.)

Part 2. Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1510. Assume σ = $254.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Lower Limit

Upper limit

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Lower Limit

Upper limit

Anystate Auto Insurance Company took a random sample of 364 insurance claims paid out during a 1-year period. The average claim paid was $1525. Assume σ = $258.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

The normal monthly precipitation (in inches) for September is listed for 20 different U.S. Cities.

3.5       1.6       2.4       3.7       4.1       3.9       1.0       3.6       4.2       3.4       3.7       2.2       1.5       4.2 3.4       2.7       0.4       3.7       2.0       3.6

Find

Mean of the data

Median of the data

Range of the data

Interquartile range of the data.   

A political scientist hypothesize that a political ad will increase attitudes about a particular issue. The scientist randomly asks 21 individuals walking by to see the ad and then take a quiz on the issue. The general public that knows little to nothing about the issue, on average, scores 50 on the quiz. The individuals that saw the ad scored an average of 51.8 with a variance of 29.05. What can the political scientist conclude with α = 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the particular issue the political ad individuals walking by general public the ad
Sample:
---Select--- the particular issue the political ad individuals walking by general public the ad

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly higher on the quiz than the general public

.Individuals that watched the political ad scored significantly lower on the quiz than the general public.    

Individuals that watched the political ad did not score significantly different on the quiz than the general public.

Consider that you toss a fair 6-sided die containing the numbers 1-2-3-4-5-6 and also toss a fair 4-sided die containing the numbers 1-2-3-4. Find the probability distribution for the sum of the values on the two dice. Also, find the mean and the variance of this probability distribution.

Please provide a well written and well explained answer.

James Madison, president of Madison Manufacturing, inc,. is considering whether to build more manufacturing plants in Madison Wisconsin. He is considering three sizes of plant: Small, Medium, or Large. At the same time, an uncertain economy makes ascertaining the demand for the new plants difficult. His management team has prepared the following cost payoff table (in thousands of dollars).

Decision Alternatives States of Nature

Good Economy Fair Economy Poor Economy Expected Value

Small plant d1 $650 $650 $600 ?

Medium plant d2 $900 $600 $300 ?

Large plant d3 $800 $650 $500 ?

Probability Factor 40% 35% 25% ?

Best decision Alternative= ?

1. Calculate the expected value for each decision alternative using Expected Value Strategy in Excel Spread Sheet.

2. Specify the best decision alternative to minimize cost.

Consider an automated plagiarism detection software that is used to evaluate essay submissions. Four sections of a writing course use the software to check for plagarism, with 30% of the students in section 1, 16% in section 2, 30% in section 3, and 24% in section 4. In section 1 of a course, 20% of the essays are flagged, in section 2, 23%, section 3, 15% and section 4, 8%. (a) What percentage of total students committed plagiarism overall? (b) Given that a particular student committed plagiarism, what in the probability that they were registered for section 1 of the course. (c) Given that a particular student committed plagiarism, what in the probability that they were registered for section 2 of the course. (d) If there are 200 students registered between these 4 sections, how many students in section 3 cheated?

For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California give the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.). x: Percentage success for mallard duck nests 11 23 44 53 65 y: Percentage success for Canada goose nests 39 15 48 15 39 (a) Use a calculator to verify that Σx = 196; Σx2 = 9,620; Σy = 156; and Σy2 = 5,796. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x, the percent of successful mallard nests. (Round your answers to two decimal places.) x s2 s (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for y, the percent of successful Canada goose nests. (Round your answers to two decimal places.) y s2 s (d) Use the results of parts (b) and (c) to compute the coefficient of variation for successful mallard nests and Canada goose nests. (Round your answers to one decimal place.) x y CV % % Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to Canada geese? The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the variance; the CV for mallard nests is higher. Would you say one group of data is more or less consistent than the other? Explain. The x data group is more consistent because the standard deviation is smaller. The two groups are equally consistent because the standard deviations are equal. The y data group is more consistent because the standard deviation is smaller.