A student runs an experiment with two carts on a low-friction track. As measured in the Earth reference frame, cart 1 (m = 0.48 kg ) moves from left to right at 1.0 m/s as the student walks along next to it at the same velocity. Let the +x direction be to the right.

a) What velocity v⃗ E2,i in the Earth reference frame must cart 2 (m = 0.16 kg ) have before the collision if, in the student's reference frame, cart 2 comes to rest right after the collision and cart 1 travels from right to left at 0.33 m/s?

b) What does the student measure for the momentum of the two-cart system?

c) What does a person standing in the Earth reference frame measure for the momentum of each cart before the collision?

A group of engineers perform an experiment to determine whether the fuel efficiency for a new type of engine for an oilfield drill is better than the most commonly used type of engine in existing oilfields. The engineers perform a 2–sample t–test and obtain a p-value of 0.04.

(i) Briefly explain what a p–value of 0.04 means (i.e. what does the p–value actually represent).

(ii) Explain what a Type II error would mean in the context of this problem.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator, type of language, and interaction. Use α = 0.05.

Find the value of the test statistic for language translator. (Round your answer to two decimal places.)

Find the p-value for language translator. (Round your answer to three decimal places.)

p-value =

State your conclusion about language translator.

Because the p-value ≤ α = 0.05, language translator is significant.Because the p-value ≤ α = 0.05, language translator is not significant.    Because the p-value > α = 0.05, language translator is not significant.Because the p-value > α = 0.05, language translator is significant.

Find the value of the test statistic for type of language. (Round your answer to two decimal places.)

Find the p-value for type of language. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of language.

Because the p-value > α = 0.05, type of language is not significant.Because the p-value ≤ α = 0.05, type of language is not significant.    Because the p-value > α = 0.05, type of language is significant.Because the p-value ≤ α = 0.05, type of language is significant.

Find the value of the test statistic for interaction between language translator and type of language. (Round your answer to two decimal places.)

Find the p-value for interaction between language translator and type of language. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between language translator and type of language.

Because the p-value > α = 0.05, interaction between language translator and type of language is not significant.Because the p-value ≤ α = 0.05, interaction between language translator and type of language is not significant.    Because the p-value ≤ α = 0.05, interaction between language translator and type of language is significant.Because the p-value > α = 0.05, interaction between language translator and type of language is significant.

An experiment was conducted to see the effectiveness of two antidotes to three different doses of a toxin. The antidote was given to a different sample of participants five minutes after the toxin. Twenty-five minutes later the response was measured as the concentration in the blood. What can the researchers conclude with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Antidote: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Dose: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Dose: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is an antidote difference in blood concentration.There is no antidote difference in blood concentration.     

There is a dose difference in blood concentration.There is no dose different in blood concentration.     

There is an antidote by dose interaction in blood concentration.There is no antidote by dose interaction in blood concentration.     

An experiment is planned where an automatic lab would be sent to the surface of Saturn. If there was life in Saturn, the probability that the lab detects it and correctly reports the finding is 0.5. If there never was life on Saturn, the probability that the lab will erroneously indicate the presence of life is 0.45. Suppose that a fair assessment of the probability that life was ever present on Saturn is 0.1.

(a) Find the probability that the lab says that there was life on Saturn.

(b) If the lab says that there was life on Saturn, what is the probability that the lab is correct (that is, that indeed there was life in Saturn)?

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 339 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status Diseased Not Diseased Total

Vaccinated 66 152 218

Not Vaccinated 84 37 121

Total 150 189 339

Step 6 of 8 : Find the critical value of the test at the 0.005 level of significance. Round your answer to three decimal places.

step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.005 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.005 level of significance.

In a dialysis experiment with a dialysis full of glucose/starch solution in a beaker of water (tested starch with iodine)- Which solutes would cross the membrane? Why were these solutes able to cross and not others? Do you have evidence that dialysis occurred? Explain. Do you have evidence that osmosis occurred? Explain. Can dialysis and osmosis occur at the same time? Why or why not?

E422: An analysis of variance (ANOVA) is used to analyze the data gathered in an experiment. Oneway ANOVA implies that this tool deals with:

I. One level

II. Independent samples

III. One dependent variable

IV. One independent variable

A. I only

B. II and III only

C. II, III, and IV only

D. I, II, III, and IV

An article in Optical Engineering reported on use of an optical correlator to perform an experiment by varying brightness and contrast. The useful range of gray levels characterizes the resulting modulation. The data are shown below:

Brightness (%): 54 61 65 100 100 100 50 57 54

Contrast (%): 56 80 70 50 65 80 25 35 26

Useful range (ng): 96 50 50 112 96 80 155 144 255

USING MINITAB...

1. Fit a multiple linear regression model to these data.
2. Estimate σ².

Which of the following is not a property of a binomial experiment?

Question 15 options:

Question 16

The probability distribution for the number of goals the Norse soccer team makes per game is given below;

Number of Goals Probability

0 0.05

1 0.15

2 0.35

3 0.30

4 0.15

Refer to the probabilities, what is the probability that in a given game the Norse will score 2 goals or more?

Question 16 options:

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

Question 20 options: