Question

Question 1:

The response time in milliseconds was determined for three different types of circuits in an electronic calculator. The results are recorded here.

Circuit Type	Response
1	19	22	20	18	25
2	20	21	33	27	40
3	16	15	18	26	17

1. Using α = 0.05, test the hypothesis that the three circuit types have the same response time. What is the p-value?
2. Analyze the residuals from this experiment.
3. If there is a significant difference, perform a Tukey test.

Question 2:

An article in Environmental International describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in showerheads. The data from the experiment are shown in the following table.

Orifice Diameter	Radon Released (%)
0.37	80	83	83	85
0.51	75	75	79	79
0.71	74	73	76	77
1.02	67	72	74	74
1.40	62	62	67	69
1.99	60	61	64	66

1. Does the size of the orifice affect the mean percentage of radon released? What is the p-value? Use α = 0.05.
2. Analyze the residuals from this experiment.
3. If there is a significant difference, perform a Tukey test.

Question 3:

In “Orthogonal Design for Process Optimization and Its Application to Plasma Etching”, an experiment is described to determine the effect of flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below.

Flow	Observations
125	2.7	4.6	2.6	3.0	3.2	3.8
160	4.9	4.6	5.0	4.2	3.6	4.2
200	4.6	3.4	2.9	3.5	4.1	5.1

1. Does flow rate affect etch uniformity? Use α = 0.05.
2. Do the residuals indicate any problems with the underlying assumptions?
3. Use the Kruskal-Wallis procedure with α = 0.05 to test for differences between mean uniformity at the three different flow rates.

Question 4:

Suppose that five normal populations have common variance σ² = 100 and means μ₁ = 175, μ₂ = 190, μ₃ = 160, μ₄ = 200, and μ₅ = 215. How many observations per population must be taken so that the probability of rejecting the hypothesis of equality of means is at least 0.95? Use α = 0.05.

Answer 1

p-value = 0.0464 Which is also less than 5% level of significance , hence we reject null hypothesis.