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 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.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 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 not 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 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 not significant.

An experiment is performed to study the fatigue performance of a high strength alloy. The number of cycles to crack initiation is measured for twenty specimens over a range of applied pseudo-stress amplitude (PSA) levels. Use the data in the table provided to fit the following three regression models with y = Cycles and x = PSA (note the natural log transform of y for all models):

PSA (x) Cycles (y)

80, 97379

80, 340084

80, 246163

80, 239348

100, 34346

100, 23834

100, 70423

100, 51851

120, 9139

120, 9487

120, 8094

120, 17956

140, 5640

140, 3338

140, 6170

140, 5608

160,    1723

160, 3525

160, 2655

160, 1732

i. A simple linear regression model: lny=β0+β1∙x .

ii. A quadratic polynomial model: lny=γ0+γ1∙x+γ2∙x2 .

iii. A simple linear regression model with a logarithm transformation on PSA: lny=δ0+δ1∙ln⁡(x) .

1. 1. For model (i.), what hypothesis being tested by the ANOVA F-test (in terms of the coefficients of the model)? Interpret the conclusion of this test in the context of the engineering problem.
2. 2. For model (ii.), what hypothesis being tested by the ANOVA F-test (in terms of the coefficients of the model)? Interpret the conclusion of this test in the context of the engineering problem.
   3. What is the p-value for testing the significance of the quadratic term in model (ii.) (Ho: γ2=0)? Interpret the conclusion of this test in the context of the engineering problem.
3. 4. Briefly discuss the advantages and disadvantages of each of the three models.

A manager of a large chain of appliance stores is planning to conduct a pricing experiment to determine the price elasticity of the chain’s line of microwave ovens. He plans to measure sales for the month of February, raise prices by 12 percent on March 15, and then measure sales for the month of April. Each sales measurement would take into account the total monthly microwave oven sales for all of the stores in his chain.

He has asked you to evaluate his research procedure and suggest any improvements. What would you suggest?

Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Twelve randomly selected plots of land were treated with fertilizer A, and

7

randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results.

Part 1 of 3

Your Answer is correct

(a) Explain why it is necessary to check whether the populations are approximately normal before constructing a confidence interval.

Since the sample size is ▼small, it is necessary to check that the populations are approximately normal.

Part 2 of 3

Your Answer is correct

(b) Following are boxplots of these data. Is it reasonable to assume that the populations are approximately normal?

400

420

440

460

480

500

520

540

360

370

380

390

400

410

420

It ▼is reasonable to assume that the populations are approximately normal.

Part: 2 / 3

2 of 3 Parts Complete

Part 3 of 3

(c) Construct an

80%

confidence interval for the difference between the mean yields for the two types of fertilizer. Let

μ1

denote the mean yield for fertilizer A. Use tables to find the critical value and round the answer to one decimal place.

1. In this experiment we injected the sample to be analyzed by Gas Chromatograph equipped with an FID (Flame Ionization Detector). The detector ionizes the sample as it reaches it, and the peak is proportional to the number of ions with a live flame. Explain in detail, why we need to run a standard when the GC is equipped with an FID detector to identify the component in a sample?

2. Gas Chromatography is another chromatography method you are learning about this semester. Construct a table comparing and contrasting the two other chromatography methods (TLC and LC). Point out to differences and similarities between each method and the GC method. Give at least 4 criteria of comparison.

3. During last week’s lab of distillation, many of you had difficulties getting the fractional distillation column to work properly. Specifically, the liquid started condensing at the top of the fractional column and the vapor did not distill over. The lab instructor suggested that changing the bead size (which was in the column) to a larger size might improve the outcome of the experiment. Is this suggestion valid? Would it help the process or is this suggestion wrong? Explain your answer.

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. Thirty 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: Reject H0 or Fail to reject H0

Dose: critical value = ___________ ; test statistic = ___________
Decision: Reject H0 or Fail to reject H0

Interaction: critical value = ___________ ; test statistic = ___________
Decision:   Reject H0 or 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.

1)There is an antidote difference in blood concentration.

2)There is no antidote difference in blood concentration.    

1)There is a dose difference in blood concentration.

2)There is no dose different in blood concentration.    

1)There is an antidote by dose interaction in blood concentration.

2)There is no antidote by dose interaction in blood concentration.    

In the Meselson - Stahl experiment, if after the first round of replication, the DNA had been denatured at high temperature before its centrifugation in a column of cesium chloride, which two models would have shown the same sedimentation pattern?

Group of answer choices

a) semiconservative and dispersive

b) none of the three would have had the same sedimentation pattern

c) all three would have shown the same sedimentation pattern

d) conservative and dispersive

e) semiconservative and conservative

In the Meselson - Stahl experiment, if after the first round of replication, the DNA had been denatured at high temperature before its centrifugation in a column of cesium chloride, which two models would have shown the same sedimentation pattern?

Group of answer choices

semiconservative and dispersive

conservative and dispersive

all three would have shown the same sedimentation pattern

semiconservative and conservative

none of the three would have had the same sedimentation pattern

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 system (Factor A), type of language (Factor B), and interaction. Use  = .05.

1. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to Factor A?
   Select:Factor A is significant, Factor A is not significant
   
3. The p-value for Factor B is Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to Factor B?
   Select: Factor B is significant, Factor B is not significant
   
4. The p-value for the interaction of factors A and B is Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to the interaction of Factors A and B?
   Select: The interaction of factors A and B is significant, The interaction of factors A and B is not significant

A social psychologist conducts an experiment to determine the best way to design a message for college students about the importance of engaging in safe sex. She hypothesizes that two factors impact the effectiveness of the message: (a) the medium used to deliver the message (lecture, video, or pamphlet), and (b) the emotional tone of the message (fear, neutral, or humor). The dependent variable is a measure of behavioral intention to engage in safe sex behavior (higher score indicating greater intention). She randomly assigns 45 participants to 9 groups, and obtains the following data:

a. Using Excel, analyze these data by performing a two-way between-groups ANOVA. Create formulas to calculate the SS terms and the rest of the ANOVA summary table.

b. Include the effect size (eta-squared) for the medium, emotional tone, and medium X emotional tone effects in your ANOVA table (you’ll need to create your own formulas).

c. Create a graph to show the results, with error bars (estimated standard error of the means).

d. Insert a textbox in which you report the results of the ANOVA, the effect sizes for any significant effects, and refer to the graph to describe the pattern of any significant results.