Explain why ρ is preferable to Cov(X,Y) in measuring the strength of relationship between X and Y
In: Statistics and Probability
Use computer software packages, such as Excel, to solve this problem.
The Jacobs Chemical Company wants to estimate the mean time (minutes) required to mix a batch of material on machines produced by three different manufacturers. To limit the cost of testing, four batches of material were mixed on machines produced by each of the three manufacturers. The times needed to mix the material follow.
Manufacturer 1  Manufacturer 2  Manufacturer 3 
17  29  17 
23  27  16 
21  32  20 
19  28  19 
a. The following regression model can be used to analyze the data.
E(y) = B0+B1D1+B2D2
Show the values of the variables below. If your answer is zero enter “0”.
D1  D2  Manufacturer 
0  0  1 
1  2  
0  3 
b. Show the estimated regression equation (to the nearest whole number and enter negative value as negative number).
y^=______+______D1 +_______D2
c. What null hypothesis should we test to determine if we should reject the assumption that the mean time to mix a batch is the same for all three manufacturers?
Select the number of the null hypothesis you would want to test.
 Select your answer 12345Item 6
d. What is the value of the test statistic in your hypothesis in part (c) (to 2 decimals)? Use Table 4 in Appendix B.
What is the value?
 Select your answer less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 8
What is your conclusion?
 Select your answer Conclude that the mean time is not the same for all three manufacturersConclude that the mean time is same for all three manufacturersItem 9
In: Statistics and Probability
For a normal population with known variance σ^{2}, what value of z_{α/2} in the Equation below gives a 98% CI?
xzα/2σn≤μ≤x+zα/2σn
In: Statistics and Probability
Binomial distributions are approximately normal when the number of trials is large, and the probaility of success is not near zero or one. A player flips an unbiased coin 1,296 times.
a. What is the probability of the coin landing on heads between 612 and 684 times?
In: Statistics and Probability
According to a survey, 63% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded. When technology is used, use the Tech Help button for further assistance.
(a) Find the probability that exactly 40 of the murders were cleared.
(b) Find the probability that between 35 and 37 of the murders, inclusive, were cleared.
(c) Would it be unusual if fewer than 18 of the murders were cleared? Why or why not?
In: Statistics and Probability
In a UnionManagement negotiation, the following are the annual percentages of wage increases for Union for various combinations of union and management strategies:
Management
M1 M2 M3
U1 1 3 3
U2 4 2 2
Union U3 3 2 3
U4 3 4 1
U5 2 1 2
9a. (5 points) After eliminating all possible dominated strategies, list the Union payoff matrices for the 4 subgames that are developed by taking 3 of the 4 Union strategies to match the 3 Management strategies.
9b. (5 points) Find the best strategy and value of the game for Union with the following payoff matrix for one of the subgames:
Management
M1 M2 M3
U2 4 2 2
Union U3 3 2 3
U4 3 4 1
9c. (10 points) We have solved in class the best strategy and value of the game for Union with the following payoff matrix for one of the subgames:
Management
M1 M2 M3
U1 1 3 3
Union U3 3 2 3
U4 3 4 1
Let q1, q2, and q3 be the respective probabilities for Management to play strategies M1, M2, and M3. Then use the same Principle of Maximin as in deraiving the best mixed strategy for Union to find the best strategy and value of the game for Management. Specifically,
9c1 (5 points) show the three independent linear equations for q1, q2, and q3.
9c2 (5 points) Show the correct solution for these 3 probabilities from these 3 independent linear equations.
In: Statistics and Probability
assume that in 2018 the mean mathematics sat score was 536 and the standard deviation was 115. a sample of 68 scores is chosen. a) what is the sampling distribution of *? b) what is the probability the sample mean score is less than 510? c) what is the probability the sample mean score is between 485 and 525? d) what is the probability the sample mean score is greater than 480? e) would it be unusual for the sample mean to be greater than 575? show work to prove your answer.
In: Statistics and Probability
In: Statistics and Probability
The transmission delay between two linked wireless devices is a normal variable with a mean of 60 milliseconds and a standard deviation of 5 milliseconds.
a. What is the probability that a transmission delay is more than 65 milliseconds?
b. What is the probability that a transmission delay is between 55 and 70 milliseconds?
c. What is the probability that a transmission delay is more than 45 milliseconds?
d. Agents for the NSA notice a transmission delay greater than 80 milliseconds. Is this a rare enough event to warrant suspicion that enemy agents are dampening the signal strength?
In: Statistics and Probability
Suppose you will perform a test to determine whether
there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r
given the number of pairs of data n and the significance level
.
n = 14, = 0.05
A; r = 0.532
B; r = ±0.532
C; r = 0.553
D; r = ±0.661
In: Statistics and Probability
A administrator wants to know what is the average starting salary, μ, for students graduating from her college. She is able to obtain data for 100 randomly selected students. For these 100 students, the average is $70,000, and the SD is $10,000. What is a 99% confidence interval for μ?
In: Statistics and Probability
a.
Which of the following is true?
Group of answer choices
Additional variables can add noise to the model that slightly increases Rsquared
All the options are true
You can use multiple independent variables to predict a dependent variable
The RSquared value is a measure of how good the model is.
b.This term refers to when two predictor variables are highly correlated with each other and so the effect of the variables on the dependent response is questionable.
In: Statistics and Probability
1. Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data.
An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1=smoothyellow,2=smoothgreen, 3=wrinkledyellow, and 4=wrinkledgreen.
Do the results make sense?
3 
1 
3 
4 
4 
1 
2 
4 
1 
4 
3 
3 
3 
3 
(a) The mean phenotype code is _____.
2. Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 10 words in a book by Terry are listed with the first 10 words in a book by David. Find the mean and median for each of the two samples, then compare the two sets of results.
Terry: 
2 
2 
2 
11 
8 
9 
2 
6 
3 
3 


David: 
3 
4 
3 
2 
3 
1 
3 
1 
4 
3 
The mean number of letters per word in Terry's book is _____.
3. Refer to the data set of times, in minutes, required for an airplane to taxi out for takeoff, listed below. Find the mean and median. How is it helpful to find the mean?
36 
35 
25 
11 
26 
29 
30 
32 
19 
39 
45 
31 

31 
14 
40 
27 
24 
48 
10 
43 
18 
30 
45 
31 

13 
34 
17 
16 
23 
40 
47 
31 
27 
34 
17 
47 

28 
35 
26 
44 
14 
43 
30 
14 
30 
18 
38 
13 
Click the icon for the taxi out takeoff data.
Find the mean and median of the data set using a calculator or similar data analysis technology.
The mean of the data set is _____ minutes.
4. Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.4 miles per hour.
Speed (miles per hour) 
42−45 
46−49 
50−53 
54−57 
58−61 


Frequency 
29 
12 
6 
3 
2 
The mean of the frequency distribution is _____ miles per hour.
5.Six different secondyear medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subject's blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation?
126 126 138 125 137 134
Range= ______ mmHg
In: Statistics and Probability
A fair die is rolled twice. Let X be the maximum of the two rolls. Find the distribution of X.
Let Y be the minimum of the two rolls. Find the variance of Y.
In: Statistics and Probability
A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness. A sample of n = 8 college students is obtained, and each student’s performance on a familiar video game (total points earned in the game) is measured before and after eating a traditional Thanksgiving dinner including roast turkey. The following table are the scores for each participant before and after the meal:
Participants: 1,2,3,4,5,6,7,8,
Before Meal (X1): 220,245,215,260,300,280,250,310
After Meal (X2) 210,220,195,265,275,290,220,285
a.For a twotailed test, what is the null hypothesis using statistical notation?
b. For a twotailed test, what is the alternative hypothesis using statistical notation?
c. What is the sum of the difference scores (D)?
d. What is the value of MD?
e. What is the value for Sum of Squares for the difference scores (SSD)?
f. What is the sample variance for the difference scores (sD 2 )?
g. What is estimated standard error (sMD)?
h. For a twotailed test with α = .05, what is the value/s for tcrit?
i. What is the value for tobt?
j. Do these data indicate a significant difference between the treatments at the .05 level of significance? NOTE: simply writing that the effect is significant (e.g., only writing “reject the null”) without showing any work/calculations in parts ae will result in point zero points.
k. Compute estimated Cohen’s d to measure the size of the treatment effect.
In: Statistics and Probability