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2 Consider the computer output shown below

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2 Consider the computer output shown below.

One-Sample T: Y

Test of mu= 91 vs. not =91

Variable N Mean Std. Dev. SE Mean 953 CI T P

Y 2592.5805 0.4673 (91.6160, 1) 3.38              0.002

(a) Fill in the missing values in the output. Can the null hypothesis be rejected at the 0.05 level? Why? (b) Is this a one-sided or a two-sided test?

(c) If the hypotheses had been Ho : µ. = 90 versus HI : µ≠  90 would you reject the null hypothesis at the 0.05 level?

(d) Use the output and the t table to find a 99 percent two-sided CI on the mean.

(e) What is the P-value if the alternative hypothesis is HI µ > 91?

 

2.27. An article in Solid State Technology, "Orthogonal Design for Process Optimization and Its Application to Plasma Etching" by G. Z. Yin and D. W. Jillie (May 1987) describes an experiment to determine the effect of the C2F6 flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. All of the runs were made in random order. Data for two flow rates are as follows:

Uniformity Observation

C2F6 Flow (SCCM)	1	2	3	4	5	6
125 200	2.7 4.6	4.6 3.4	2.6 2.9	3.0 3.5	3.2 4.1	3.8 5.1

 

 (a) Does the C2F6 flow rate affect average etch uniformi-ty? Use a = 0.05.

(b) What is the P-value for the test in part (a)?

(c) Does the C2F6 flow rate affect the wafer-to-wafer vari-ability in etch uniformity? Use a = 0.05.

(d) Draw box plots to assist in the interpretation of the data from this experiment.

 

1. Suppose that you want to compare the growth of garden flowers with different conditions of sunlight, water, fertilizer, and soil conditions. Complete steps 1-3 of the guidelines for designing experiments as shown in the textbook and notes.

2.1. Computer output for a random sample of data is shown below. Some of the quantities are missing. Compute the values of the missing quantities.

variable	N	Mean	SE Mean	Std  Dev.	Variance	Min.	Max.
Y	9	19.96	?	3.12	?	15.94	27.16

 

2.3. Suppose that we are testing H₀ : µ = µ₀ versus H_1:µ≠µ₀. Calculate the P-value for the following observed values of the test statistic:

 (a) Z₀ = 2.25  (c) Z₀ = 2.10 (e) Z₀ = —0.10

2.5. Consider the computer output shown below.

One-Sample Z

Test of mu = 30 vs not = 30

The assumed standard deviation = 1.2

N  Mean      SE Mean    95%      CI                Z  P

16 31.2000 0.3000     (30.6120, 31.7880)

(a) Fill in the missing values in the output.  What conclusion would you draw?

(b) Is this a one-sided or two-sided test?

(c) Use the output and the normal table to find a 99 percent CI on the mean.

(d)What is the P-value if the alternative hypothesis is H₁ : µ, > 30?

 

2.20. The shelf life of a carbonated beverage is of interest. Ten bottles are randomly selected and tested, and the following results are obtained:

Days

108                  138

124                  163

124                  159

106                  134

115                  139

 

 (a) We would like to demonstrate that the mean shelf life exceeds 120 days. Set up appropriate hypotheses for investigating this claim.

(b) Test these hypotheses using a = 0.01. What are your conclusions?

(c) Find the P-value for the test in part (b).

(d) Construct a 99 percent confidence interval on the shelf life.