[Solved] Assignment 1 STA6246 Design and Analysis of Experiments

Solve the following problems.

1. Why is randomization important in an experiment? Give an example.
2. Select an experiment of interest to you. State the problem, then select the response variable,and choose the factors, levels, and ranges.
3. Consider the computer output shown below.
   • Fill in the missing values in the output. What conclusion would you draw?
   • Is this a one-sided or two-sided test?
   • Use the output and the normal table to find a 99% Confidence Interval of the populationmean.
   • What is the P-value if the alternative hypothesis is H₁: ₁ > 30?
4. The breaking strength of a fiber is required to be at least 150 psi. Past experience hasindicated that the standard deviation of breaking strength is = 3 psi. A random sample of four specimens is tested, and the results are y₁ = 145,y₂ = 153,y₃ = 150,y₄ = 147.
   • State the hypotheses that you think should be tested in this experiment. Test thesehypotheses using = 0.
   • What is the test statistic?
   • What are the critical values?

1

• What is the P-value?
• What are your conclusions?
• Find a 95% Confidence Interval of the population mean breaking strength.