A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 840 m apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 m/s2. Is there a collision? If so, give (a) the speed of the red train, (b) the speed of the green train, and (c) the separation between the trains when they collide (0 m). If not, give (a) the speed of the red train (0 m/s), (b) the speed of the green train (0 m/s), and (c) the separation between the trains when they stop.

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. It gives the wait-times in minutes.

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others.

H₀:  μ₂ > μ₃ > μ₁.    

H₀:  μ₁ = μ₂ = μ₃.

H₀:  μ₁ ≠ μ₂ ≠ μ₃.

(b) What is the alternate hypothesis for this test?

H₁: At least one of the population means is different from the others.

H₁:  μ₁ ≠ μ₂ ≠ μ₃.    

H₁:  μ₂ > μ₃ > μ₁.

H₁:  μ₁ = μ₂ = μ₃.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that all of the mean wait-times are the same.

There is sufficient evidence to conclude that the mean wait-times are different.    

There is not enough evidence to conclude that the mean wait-times are different.

(f) Does your conclusion change at the 0.01 significance level?

Yes

No    

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. It gives the wait-times in minutes.

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others. H₀: μ₁ = μ₂ = μ₃.     H₀: μ₁ ≠ μ₂ ≠ μ₃. H₀: μ₂ > μ₃ > μ₁.

(b) What is the alternate hypothesis for this test?

H₁: μ₁ ≠ μ₂ ≠ μ₃. H₁: At least one of the population means is different from the others.     H₁: μ₁ = μ₂ = μ₃. H₁: μ₂ > μ₃ > μ₁.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis at the 0.01 significance level?

reject H₀ fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that all of the mean wait-times are the same. There is sufficient evidence to conclude that the mean wait-times are different.     There is not enough evidence to conclude that the mean wait-times are different.

(f) Does your conclusion change at the 0.10 significance level?

Yes No    

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. It gives the wait-times in minutes.

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

(a) What is the null hypothesis for this test?

H₀:  μ₂ > μ₃ > μ₁.H₀:  μ₁ ≠ μ₂ ≠ μ₃.    H₀: At least one of the population means is different from the others.H₀:  μ₁ = μ₂ = μ₃.

(b) What is the alternate hypothesis for this test?

H₁:  μ₁ = μ₂ = μ₃.H₁: At least one of the population means is different from the others.    H₁:  μ₂ > μ₃ > μ₁.H₁:  μ₁ ≠ μ₂ ≠ μ₃.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that all of the mean wait-times are the same.There is sufficient evidence to conclude that the mean wait-times are different.    There is not enough evidence to conclude that the mean wait-times are different.

(f) Does your conclusion change at the 0.01 significance level?

YesNo    

2.

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. It gives the wait-times in minutes.  

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

(a) What is the null hypothesis for this test?

H₀:  μ₁ ≠ μ₂ ≠ μ₃.H₀: At least one of the population means is different from the others.     H₀:  μ₁ = μ₂ = μ₃.H₀:  μ₂ > μ₃ > μ₁.

(b) What is the alternate hypothesis for this test?

H₁: At least one of the population means is different from the others.H₁:  μ₁ ≠ μ₂ ≠ μ₃.     H₁:  μ₁ = μ₂ = μ₃.H₁:  μ₂ > μ₃ > μ₁.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis at the 0.05 significance level?

reject H₀fail to reject H₀     

(e) Choose the appropriate concluding statement.

We have proven that all of the mean wait-times are the same.There is sufficient evidence to conclude that the mean wait-times are different.     There is not enough evidence to conclude that the mean wait-times are different.

(f) Does your conclusion change at the 0.01 significance level?

YesNo     

The following questions were not following an experiment. They are able to be answered without more information.

2. In free-raducal halogenation reaction, one can predict the relative amounts of the possible products using a simple equation: (probability factor to form a given product)x(reactivity factor)=relative amount of that product For example: consider the monochlorination of propane. Two products are possible: 1-chloropropane and 2- chloropropane. Replacing any of the six 1 hydrogen gives 1- chloropropane and replacing either of the two 2 hydrogens will give 2- chloropropane. Therefore, the probability factor for forming 1- chloropropane is 6 and the probability factor forming 2- chloropropane is 2. The relative reactivity factors for chlorine are, for 1, 2, and 3 C-H bonds, 1.0, 3.5, and 5.0, respectively. If butane is subjected to free-radical chlorination, what would be the relative ratios of 1- chlorobutane and 2- chlorobutane?

3. Calculate the relative product ratios for the free-radical bromination of butane. The reactivity factor for 1, 2, and 3 C-H bonds with bromine are 1.0, 82, and 1600, respectively.

4. Calculate the relative ratios of products for the monochlorination of 2-methylpropane. Remember to determine how many ways a particular product could be produced (how many different hydrogens could be replaced to give the same product). Hint: Drawing out the starting material and the possible products may be helpful.

5. Calculate the relative ratios of products for the monochlorination of 2,4-dimethylpropane. Remember to determine how many ways a particular product could be produced (how many different hydrogens could be replaced to give the same product). Hint: Drawing out the starting material and the possible products may be helpful.

Your Fan retails computer fans in two sizes: small and large. The business has provided you with the following information for a regular month of trading:

Business owners are considering selling computer fans in one size only. Retailing one fan size would mean lower purchase cost and selling price per unit and larger monthly sales volume. The table below reflects how trading would change if only small or large fans were sold.

Required:

For each of the three scenarios (selling both fans, selling small fans only, and selling large fans only), calculate the expected monthly profit.

Answer here:

Expected monthly profit if selling both fans:

Expected monthly profit if selling small fans only:

Expected monthly profit if selling large fans only:

Your Fan decides to switch to retailing small fans only. What would the monthly sales volume (in dollar value) need to be to generate a monthly profit that is double of the monthly fixed cost?

1. A student majoring in Health Sciences with a minor in Sports Medicine wanted to see if there was a linear relationship between the height and weight of male professional athletes.

a) Using the equation for the line of best fit determine the weight of a male professional athlete that is 75 inches tall. If you cannot determine the answer, please give a reason why.
b) What is the slope? What does it represent in this example? (4 points)

c) What is the y-intercept? What does it represent in this example? Is it meaningful?

d) Can you accurately predict the weight of a male professional athlete who is 60 inches tall? Please give a reason for your answer

e) Interpret what R-Sq means in this example and find the linear correlation coefficient r.

f. Determine the weight of a woman professional basketball who height is 72 inches. If you can’t make the prediction please explain why you can’t.

2. A nursing student randomly selected 30 States and created the following graph.

A student claims the linear correlation coefficient is r = - 0 .97.   

a. Explain how you know that the student is incorrect?
b. Another student claims the linear correlation coefficient is r = 1.01. How do you know this student is incorrect?

3.
a) Which of the following is the best estimate for the value of the linear correlation coefficient r ? 1) r is between –1.0 and –0.5 2) r is between –0.5 and 0 3) r is between 0 and 0.5 4) r is between 0.5 and 1.0

b) Estimate the income for someone who has 15 years of experience.

c) True or false: The scatterplot shows years of experience caused a person’s income to increase.

The Institute of Econometric Excellence’s report “Adult Males Living with Parents” states the following:

The examination of the percentage of males aged 25-34 living with their parents across 1000 US cities reveals that three economic and three sociological variables were deemed determinative. In a solely economic regression model, called Model E, the three economic variables alone explained 45% of the changes in cohabitation. In a solely sociological regression model, called Model S, the three sociology variables alone explained 47% of the changes in cohabitation. To determine whether the economic variables added any predictive power to Model S, and to avoid variables confounding one another, the researchers added the predicted percentages of cohabitation from Model E to Model S. The coefficient for predicted cohabitation was 2.5 with a standard error of 1.0. The authors then added the predicted percentages of cohabitation from Model S to Model E and found that the coefficient for predicted cohabitation was -3.0 with a standard error of 1.0.

The econometric term for the problem of variables “confounding” one another is a)________ (serial correlation/multicollinearity/heteroscedasticity) and it would appear in regression results in in terms of b)_______ (VIFs exceeding 5/Durbin-Watson statistic near 2/failing to reject the H0 of a White test).

The test procedure the researchers are running by adding the predicted cohabitation variables to different regression models is the c)________ (Ramsey RESET /Davidson-MacKinnon J/Quandt-Andrews Breakpoint test).

According to these results, if our sole desire is to accurately predict the percentage of cohabitation in a city, the variables that should be included in a regression model are the d)________ (sociology only/economic only/sociology and economic) because the test reveals the e)_______ (sociology only/economic only/sociology and economic) are statistically significant.