Assignment_Design of experiment analysis
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Make sure CLARIFY/JUSTIFYyour answers with concise phrase or word
1) A large laboratory has four types of devices used to determine the pH of soil samples. Thelaboratory wants to determine whether there are differences in the average readings given bythese devices. The lab uses 24 soil samples having known pH in the study and randomly assignssix of the samples to each device. The soil samples are tested, and the response recorded for eachsample is the difference between the pH reading of the device and the known pH of the soil.These values, along with summary statistics, are given in the following table.

 Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices?
 Run an analysis of variance to confirm or reject your conclusion in part (a). use a α=.05.
 Compute the pvalue of the F test in part (b).
 What conditions must be satisfied for your analysis in parts (b) and (c) to be valid?
 Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?
2) A computer ANOVA output is shown below. Fill in the blanks. Please may give bounds on the Pvalue.Provide your calculation details.
Oneway ANOVA Source DF SS MS F P Factor 3 36.15 ? ? ? Error ? ? ? Total 19 196.04 
3)The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected:
Mixing Technique 
Tensile Strength (lb/in2) 

1 
3129 
3000 
2865 
2890 

2 
3200 
3300 
2975 
3150 

3 
2800 
2900 
2985 
3050 

4 
2600 
2700 
2600 
2765 
 Test the hypothesis that mixing techniques affect the strength of the cement. Use α=0.05.Complete the calculation manually.
 Construct boxplots display to compare the mean tensile strengths for the four mixing techniques. What are your conclusions?
 Construct a normal probability plot. What conclusion would you draw about the validity of the normality assumption?
4) Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05.Complete the calculation manually.
5) Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below.
Test the claim that the four different models have the same population mean. Use a significance level of 0.05.Complete the calculation manually.
6) Use the data given below to verify that the t test for independent samples and the ANOVA method are equivalent.
i) Use a t test with a 0.05 significance level to test the claim that the two samples come from populations with the same means.
ii) Use the ANOVA method with a 0.05 significance level to test the same claim.
iii) Verify that the squares of the t test statistic and the critical value are equal to the F test statistic and critical value.

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Solution: A large laboratory has four types of devices used to determine