A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=12 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05.

   X1          X2         Y

R2=
F=
P-value for overall model =

t1=
for b1, P-value =
t2=
for b2, P-value =

What is your conclusion for the overall regression model (also called the omnibus test)?

• The overall regression model is statistically significant at α=0.05

• The overall regression model is not statistically significant at α=0.05

Which of the regression coefficients are statistically different from zero?

• neither regression coefficient is statistically significant
• the slope for the first variable b1 is the only statistically significant coefficient
• the slope for the second variable b2 is the only statistically significant coefficient
• both regression coefficients are statistically significant

2. Given the following descriptive statistics,

N=18

X bar = 11.5

S sub x = 2

a. find the 95% confidence interval of the population mean u.

b. Suppose you know the population standard deviation = 2. What is the minimum sample size that makes the confidence interval length less than 1?

Q4) A desk lamp produced by The Luminar Company was found to be defective (D). There are three factories (A, B, C) where such desk lamps are manufactured. A Quality Control Manager is responsible for investigating the source of found defects. They know that factory A supplies 50% of the total lamps, factory B supplies 30% of the total lamps, and factory C supplies 20% of the total lamps. They also know that on average, 2.0% or factory A’s lamps are defective, 1.0% of factory B’s lamps are defective, and 3.0% of factory C’s lamps are defective. If a randomly selected lamp is defective, what is the probability that it was manufactured in factory A? If a randomly selected lamp is defective, what is the probability that it was manufactured in factory B? If a randomly selected lamp is defective, what is the probability that it was manufactured in factory C? If a randomly selected lamp is not defective, what is the probability that it was manufactured in factory A?

Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. At the 0.01 significance level, does the data below show significant (linear) correlation between X and Y?

• Yes, significant correlation
• No

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=16 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.05.

X1             X2             Y

SSreg=
SSres=
R2=
F=
P-value =

What is your decision for the hypothesis test?

• Reject the null hypothesis, H0:β1=β2=0

• Fail to reject H0

What is your final conclusion?

• The evidence supports the claim that one or more of the regression coefficients is non-zero
• The evidence supports the claim that all of the regression coefficients are zero
• There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
• There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero

Dr. Stambaugh hypothesizes that a novel anxiety drug will affect memory. To examine this, the drug is administered to a random sample of 23 trained rats. The rats were then placed in a maze and timed on how long it took them to complete it. The average completion time was 47 seconds. Normal rats have an average completion time of 44 seconds with a standard deviation of 14 seconds. What can Dr. Stambaugh conclude with α = 0.01?

a) State the appropiate appropriate test statistic (na, z-test, one sample t test, independent- samples t test, related sample t test), population (normal rats, memory, trained rats, time to complete maze, the maze), and sample (normal rats, memory, trained rats, time to complete maze, the maze).
.


b) 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

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

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

Now, Make an interpretation based on the results.

Rats on the anxiety drug were significantly slower completing the maze.

Rats on the anxiety drug were significantly quicker completing the maze.    T

he anxiety drug did not affect rats in completing the maze.

9.3.3

A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level.

Table #9.3.5: Total Brain Volume (in mm3) of Normal Patients

Table #9.3.6: Total Brain Volume (in mm3) of Schizophrenia Patients

9.3.4

A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.

9.3.8

The number of cell phones per 100 residents in countries in Europe is given in table #9.3.9 for the year 2010. The number of cell phones per 100 residents in countries of the Americas is given in table #9.3.10 also for the year 2010 ("Population reference bureau," 2013). Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas.

Table #9.3.9: Number of Cell Phones per 100 Residents in Europe

Table #9.3.10: Number of Cell Phones per 100 Residents in the Americas

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 46% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 26 strikes. Find the following probabilities. (Round your answers to four decimal places.)

(a) 12 or fewer fish were caught


(b) 5 or more fish were caught


(c) between 5 and 12 fish were caught

The following data show the brand, price, and the overall score for six stereo headphones that were tested by consumer reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 to 100.

Price Score

Bose 180 76

Skullcandy 150 71

Koss 85 61

Phillips/O'Neill 70 56

Denon 70 40

JVC 35 26

a). Test for a significant relationship using the F test. What is your conclusion? Use α= 0.05

b). Develop a point estimate of the score for a headphone with a price of 100.

c). Develop a 95% confidence interval for the mean score for all headphones with a price of 100.

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 80 hours and a standard deviation of 9 hours. Complete parts a through c.

a. What is the probability that a single battery randomly selected from the population will have a life between 7575 and 85 ​hours?

b. What is the probability that 99 randomly sampled batteries from the population will have a sample mean life of between 75 and 85 ​hours?

c. If the manufacturer of the battery is able to reduce the standard deviation of battery life from 9 to 7 ​hours, what would be the probability that 9 batteries randomly sampled from the population will have a sample mean life of between 75 and 85 ​hours?

Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.42, on one serving of Dial 911, $0.55. Each serving of Wimpy requires 0.22 pound of beef, 0.22 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.22 pound of beef, 0.37 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 17 pounds of beef, 12 cups of onions, 86 ounces of Kilgore’s special sauce, and 57 ounces of hot sauce on hand.

A) Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let W = number of servings of Wimpy to make D = number of servings of Dial 911 to make

B) Find an optimal solution. If required, round your answers to two decimal places.

W = , D = , Profit = $

C) What is the shadow price for special sauce? If required, round your answers to two decimal places. $ Interpret the shadow price.

D) The input in the box below will not be graded, but may be reviewed and considered by your instructor. Increase the amount of special sauce available by 1 ounce and re-solve. If required, round your answers to two decimal places.

W = , D = , Profit = $

At the .05 significance level, does the data below show significant correlation?

• Yes, significant correlation
• No

1) TRUE OR FALSE: Parameters yield populations

2) TRUE OR FALSE: In a study entitled the relationship between study time and grades, study time is the predictor variable.

3) TRUE OR FALSE: Only experiments involve direct measurement by the researcher.

4) A response variable is also an outcome variable.

5) Statistical methods that use sample data to make statements about populations are called inferential statistics.

6) The IV is the variable that can be randomly assigned by the researcher.

We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2.

• HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error.
• RBI - Run batted in - number of runners who scored due to a batters' action, except when batter grounded into double play or reached on an error
• Salary is in millions of dollars.

The following is a chart of baseball players' salaries and statistics from 2016.

a) Use software to find the multiple linear regression equation. Enter the coefficients rounded to 4 decimal places.
ˆy= ______ + _____ x1 + ______ x2

b) Use the multiple linear regression equation to predict the salary for a baseball player with an RBI of 31 and HR of 20. Round your answer to 1 decimal place, do not convert numbers to dollars.
      ________ millions of dollars

c) Holding all other variables constant, what is the correct interpretation of the coefficient b1=0.111 in the multiple linear regression equation?

• For each HR, a baseball player's predicted salary increases by 0.111 million dollars.
• For each RBI, a baseball player's predicted salary increases by 0.111 million dollars.
• If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by one.
• If the baseball player's salary increases by 0.111 million dollars, then the predicted RBI will increase by 0.0371.

d) Holding all other variables constant, what is the correct interpretation of the coefficient b2=0.0371 in the multiple linear regression equation?

• If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by one.
• If the baseball player's salary increases by 0.0371 million dollars, then the predicted HR will increase by 0.111.
• For each RBI, a baseball player's predicted salary increases by 0.0371 million dollars.
• For each HR, a baseball player's predicted salary increases by 0.0371 million dollars.

Problem 3-25 (Algorithmic) The College Board National Office recently reported that in 2011–2012, the 547,038 high school juniors who took the ACT achieved a mean score of 540 with a standard deviation of 122 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf/research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed.

What is the probability that a high school junior who takes the test will score no higher than 470 on the mathematics portion of the test? If required, round your answer to four decimal places.

P (x ≤ 470) =

What is the probability that a high school junior who takes the test will score between 470 and 550 on the mathematics portion of the test? If required, round your answer to four decimal places.

P (470 ≤ x ≤ 550) =