A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago. Five years ago, a sample of 270 students showed that 120 considered themselves overweight. This year a poll of 300 students showed that 140 considered themselves overweight. At a 5% level of significance, test to see if there is any difference in the proportion of college students who consider themselves overweight between the two polls. What is your conclusion?

Q: A computer consulting firm presently has bids out on three projects. Let A_i = {awarded project i}, for i = 1, 2, 3, and suppose that P(A₁) = 0.23, P(A₂) = 0.25, P(A₃) = 0.29, P(A₁ ∩ A₂) = 0.07, P(A₁ ∩ A₃) = 0.05, P(A₂ ∩ A₃) = 0.08, P(A₁ ∩ A₂ ∩ A₃) = 0.02. Use the probabilities given above to compute the following probabilities, and explain in words the meaning of each one. (Round your answers to four decimal places.)

(a)    P(A₂ | A₁) =

Explain this probability in words.

If the firm is awarded project 2, this is the chance they will also be awarded project 1. If the firm is awarded project 1, this is the chance they will also be awarded project 2.     This is the probability that the firm is awarded either project 1 or project 2. This is the probability that the firm is awarded both project 1 and project 2.

(b)    P(A₂ ∩ A₃ | A₁) =

Explain this probability in words.

This is the probability that the firm is awarded projects 1, 2, and 3. If the firm is awarded project 1, this is the chance they will also be awarded projects 2 and 3.     If the firm is awarded projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded at least one of the projects.

(c)    P(A₂ ∪ A₃ | A₁) =

Explain this probability in words.

If the firm is awarded project 1, this is the chance they will also be awarded at least one of the other two projects. This is the probability that the firm is awarded at least one of the projects.     If the firm is awarded at least one of projects 2 and 3, this is the chance they will also be awarded project 1. This is the probability that the firm is awarded projects 1, 2, and 3.

(d)    P(A₁ ∩ A₂ ∩ A₃ | A₁ ∪ A₂ ∪ A₃) =

Explain this probability in words.

This is the probability that the firm is awarded at least one of the projects. This is the probability that the firm is awarded projects 1, 2, and 3.     If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Q: Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.38 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar.

(a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.)

(b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.)

Use the cumulative distribution function of X to calculate

P(2 ≤ X ≤ 7).

(Round your answer to four decimal places.)

P(2 ≤ X ≤ 7) =

I need the correct excel equation for this question:

A toy company buys large quantities of plastic pellets for use in the manufacturing of its products. The production manager wants to develop a forecasting system for plastic pellet prices and is considering four different approaches and 6 different models. He plans to use historical data to test the different models for accuracy. The price per pound of plastic pellets (actual) has varied as shown:

SIMPLE LINEAR REGRESSION

• Use all of the data, months 1-16, to calculate the regression equation for this data. Use the months (1-16) as the independent variable (x) and price as the dependent variable (y). Once you have the equation, forecast months 7-16 (enter 7, 8, etc. as the x value in the equation). Calculate the MAD for this forecasting model. Comment on the goodness of fit (R²) and significance of the model (F significance) to determine if this forecast model should be included in the consideration of the different approaches. (If the model is not significant, it cannot be considered, however, you must still make the forecasts and calculate the MAD).

A well-known brokerage firm executive claimed that at least 24 % of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that out of 144 randomly selected people, 42 of them said they are confident of meeting their goals.

Perform a hypothesis test. Cleary label and show all four steps.

(a) List three criteria to make decision about the null hypothesis in inferential statistics. (b) When will you reject the null hypothesis using those criteria?

Use the following info for Questions 6-10.

Classic Golf, Inc., manages five golf courses in Florida. The director wishes to compare the rounds of golf played at the five courses, so he counted the rounds for a sample week. At the .05 significance level, is there an actual difference in the numbers of rounds playd at the five courses?

• H₀ : the #rounds played at the five courses is the same
• H₁: the #rounds played at the five courses is not the same

(Part of the data analysis is provided for you.)

Course     #Rounds played     (fe)     (fo - fe)     (fo - fe)²     (fo -fe)²/fe

Dogwood              124          104       20             400             3.846

Forsythia                74          104      -30             900             8.654

Starburst               104

Azalia                     98

Sunflower              120   

Golf Course Question #6: how was (fe) calculated?

QUESTION 7

1. Golf Course Question #7: Calculate ∑( fo - fe) ²

   	A.	1590
   	B.	1592
   	C.	1594
   	D.	1596

QUESTION 8

1. Golf Course Question #8: What is the critical value of Chi-Square?

   	A.	9.263
   	B.	9.488
   	C.	11.070
   	D.	15.211

Golf Course Question #9: What is the computed value of Chi-Square?

QUESTION 10

1. Golf Course Question #10: What is your decision?

   	A.	#Rounds played is the same at all 5
   	B.	#Rounds played is not the same at all 5
   	C.	Cannot be determined

What is the correlation between the number of calories consumed and BMI?

What is the slope coefficient for the linear relationship between the number of calories consumed and BMI, assuming that caloric intake is the independent variable? Round answer to 3 decimal places.

What is the intercept for the linear relationship between the number of calories consumed and BMI, assuming caloric intake is the independent variable?

Which of the following can you conclude based on your analyses?a) consumption of more calories leads to greater BMI b) consuming more calories leads to lower BMI c) calorie consumption has no relationship

The time in hours that a technician requires to perform preventative maintenance on an air conditioning unit has a mean time of one (1) hour and a standard deviation also of one (1) hour. Your company has a contract to maintain 70 of these units in an apartment building. You must schedule technicians' time for a visti to this building.

Consider the 70 air conditioners as a simple random sample from all air conditioning units of this type.

a. What is the samplng distribution for the mean time spent working on these air conditioning units. Remember a distribution describes the shape center and spread. Explain fully.

b.What is the probability that the average maintenance time spent on these 70 units exceeds 1.1 hours?
Enter your final answer below, Round to 4 decimal places.

c. What is the probability that the average maintenance time spent on these 70 units exceeds 1.25 hours?

d. Is it safe to budget an average of 1.1 hours for each unit? Or should you budget an average of 1.25 hours for each unit? Why?

Problem 12-14 (Algorithmic)

The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $36,000. The variable cost for the product is uniformly distributed between $20 and $28 per unit. The product will sell for $56 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1,200 units and a standard deviation of 100 units. Develop an Excel worksheet simulation for this problem. Use 500 simulation trials to answer the following questions:

1. What is the mean profit for the simulation? Round your answer to the nearest dollar.
   
   Mean profit = $ ___
2. What is the probability that the project will result in a loss? Recalculate the numerical value of probability in percent and then round your answer to the nearest whole number.
   
   Probability of Loss =____ %

Order in choice. Does the order in which wine is presented make a
difference? Several choices of wine are presented one at a time and in sequence,
and the subject is then asked to choose the preferred wine at the end of the
sequence. In this study, subjects were asked to taste two wine samples in
sequence. Both samples given to a subject were the same wine, although subjects
were expecting to taste two different samples of a particular variety. Of the 32
subjects in the study, 22 selected the wine presented first, when presented with
two identical wine samples.
29

(a) Do the data give good reason to conclude that the subjects are not equally
likely to choose either of the two positions when presented with two
identical wine samples in sequence?
(b) The subjects were recruited in Ontario, Canada, via advertisements to
participate in a study of “attitudes and values toward wine.” Can we
generalize our conclusions to all wine tasters? Explain

What are the factors that affect the magnitude of correlation coefficient? (a) List at least 2 factors and (b) explain how they affect the magnitude of correlation coefficient.

A travel magazine conducts an annual survey where readers rate their favorite cruise ship. Ships are rated on a 10 point scale, with higher values indicating better service. A sample of 55 ships that carry fewer than 500 passengers resulted in a average rating of 6.36 with standard deviation 0.63. A sample of 25 ships that carry more than 500 passengers resulted in an average rating of 6.12 with standard deviation 0.78.

Give a 95% confidence interval of the difference between the population mean ratings for smaller ships and the population mean ratings for larger ships. (Note, the order of subtraction matters...look at the wording carefully.)

±±  Rounded to 2 decimal places.

A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 53. Another random sample of 21 trucks were fitted with the old fuel injection system and driven under a variety of different conditions. For these trucks, the sample variance of gasoline consumption was 33.1. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Use a 5% level of significance. How could your test conclusion relate to the question regarding the consistency of fuel consumption for the two fuel injection systems?

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.    The populations follow independent normal distributions.The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.2000.100 < P-value < 0.200    0.050 < P-value < 0.1000.020 < P-value < 0.0500.002 < P-value < 0.020P-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems.Reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems.    Reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems.Fail to reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems.

Find a study that uses linear regression and a line of best fit. What is the Correlation Coefficient? What conclusions can you make about the data? Is there a correlation and how strong is it?