homework

Note: Please work with Excel and submit printed. Interpretation of the results are as important as the analysis itself. Therefore, please comment on the results.

1. Use the provided data to conduct a hypothesis testing on the population proportion. The firm firmly believes that their defect rate is 15%. For the definition of a defective part, any part that has measures outside of [12.6, 13.4] are considered a defect. (See the blackboard HW03 AssignmentData file ≫ ProportionData Worksheet).

A. Use Data Analysis ToolPak to draw simple random sample with size of 30 for five times[footnoteRef:2]. For each draw, please calculate the proportion of the defect in the sample. These will be your estimator of the population proportion. [2: In the classroom demo I did on 02/17, I only used a sample size of 10. But, just be reminded that here in the actual problem, I am asking you to use the sample of 30. That is n = 30. Your margin of error should be smaller than n = 10. ]

B. Construct the 95% confidence interval for each of these sample proportion.

a. The sampling distribution of the population proportion assumes a normal distribution with the mean of and the standard error of . When is not known, one can use to approximate the value of p.

C. How many times (out of the five times) did you find that the hypothesized true proportion of 15% are within the constructed confidence interval?

D. Please discuss your finding about the sampling process (describe your observations) as well as your verdict on the firm’s claim.

Hint: After calculation of the margin of error, you will need to complete a table like this for question A-C. Complete the table in Excel, and then paste it in Word to complete. (Paste as an image will save you much hassle) Update 02/19/2020: I added an Excel formula that can help you solve the most part of this problem. Please go check the Blackboard where you have downloaded this document.

2. Maggie’s French Fry Study. It is a case from the textbook: page 305. You can find the data at “Data Files for Problems” section of the Blackboard. Please read the case to understand the context of the problem. Then, instead of working on the problems of the book, please conduct following two tests:

a. Compare the mean of two different locations (1 and 2). Then establish a statistical significance on your results. Please comment on your results.

b. Compare the non-conforming rate between two locations. Then establish a statistical significance on your results. Please comment on your results.

c. Assume that one of your tests returned a p-value of .051 while α is .05. Would you be very confident in rejecting/accepting such results?

d. Assume that your p-value was larger than the α by a good margin. Naturally, you would report that null hypothesis cannot be rejected. But, briefly discuss about the type of error you will be making by doing so. (Hint: look-up Type I and Type II error.)

3. Use ANOVA-Twoway Data, please conduct a Twoway ANOVA analysis and offer some discussion required below. Please choose GlassType 2 3 and Temp 100 and 150 (2 by 2 design) as the experiment data.

a. Conduct a Twoway ANOVA using Excel and Paste the result in picture in the space below. Please comment on the result. Which one is the sample factor, and which one is the column factor? Please discuss.

b. What is the amount of total variations that can be explained by these two factors? (Hint: look for the ratio between SSTR/SST)

c. Is there any factor(s) turn out to be not introducing any variations to the responses? (Hint: judging by the p-value associated with the factor?

d. Please plot the interaction and paste it here. And offer some explanations.

e. What happens to the response when it jumps from Low-low treatment to high-high treatment? Show the calculation.

4. Please conduct a linear regression with the same data (GlassType 2 and 3, and Temp 100 and 150, and their responses. Your GlassType variable will have 2 and 3, Temp variable will have 100 and 150. Hint: you need to move these data to a new worksheet to start new.) A linear regression follows the following equation:

(Therefore, they follow this type of explanations: “When all other variables remain the same, with 1 unit increase in , you will see unit increase in the response variable. )

a. Run the regression tool from the Excel and paste the result in here.

b. Please comment on the statistical significance of the model, coefficients (beta 1 and beta 2), the percentage of variations in response variable that is explained by the factor.

c. Please try to interpret the result here. “With other variables remain the same, with 1 unit increase in the variable 1, accompanies, ___ units in the response variable”

d. Base on your model, please predict the following:

1) What is the amount of light output, when GlassType is 1 and Temp is 100?

2) What is the amount of light output, when GlassType is 2 and Temp is 150?

3) What is the difference between 1) and 2)?

e. What your answer in 4-d-3) matches 3-e? They are supposedly asking the same thing. If not the same, what seems to be the issue? Please discuss.