Q1) A two?sample t?test has been conducted and the sample sizes are n1 = n2 = 10

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Q1) A two?sample t?test has been conducted and the sample sizes are n₁ = n₂ = 10. The computed value of the test statistic is t₀ = 3.60. If the null hypothesis is one?sided, an upper bound on the P?value is

0.005

0.1

0.025

0.01

None

Q2

The mean square for error in the ANOVA provides an estimate of 

The variance of the random error

The variance of an individual treatment average

The standard deviation of an individual observation

None of the above

Q3

If a test of hypothesis has a Type I error probability of 0.02, what does this mean?

		If the null hypothesis is true, we do not reject it 2% of the time.
		If the null hypothesis is true, we reject it 2% of the time.
		If the null hypothesis is false, we do not reject it 2% of the time.
		If the null hypothesis is false, we reject it 2% of the time.

 

Q4

Suppose that a single?factor experiment with six levels of the factor has been conducted. There are four replicates and the experiment has been conducted in blocks. The error sum of squares is 600 and the block sum of squares is 300. If the experiment had been conducted as a completely randomized design the estimate of the error variance σ² would be. 

		None of these
		35.0
		50.0
		25.5
		37.5

 

Q5

Consider a single?factor experiment with five levels of the factor. There are four replicates and the experiment has been conducted as a complete randomized design. If the experiment had been conducted in blocks, the pure error degrees of freedom would be reduced by

		4
		5
		3
		2
		None of these

 

Question 6.

A graduate student has conducted a complete randomized design with a single factor, hoping to solve the mystery of the unified theory and complete her thesis. The results of this experiment are summarized in the following ANOVA display: 
Source llF SS MS 
Factor Error 35.76 Total 21 102.48 
11.15 
Answer the following questions about this experiment. (2 points for each of a—j) a. The sum of squares for the factor is b. The number of degrees of freedom for the single factor in the experiment is c. The number of degrees of freedom for error is d. The mean square for error is e. The value of the test statistic is f. If the significance level is 0.05, your conclusions are not to reject the null hypothesis. (Yes or No) g. An upper bound on the P-value for the test statistic is h. A lower bound on the P-value for the test statistic is i. Laura used _levels of the factor in this experiment. 

Question 7:

Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Observations are taken for four days, and the data are shown here. 
Days Solution 1 13 16 8 2 22 24 5 3 18 17 4 4 39 44 22 1 3 
(a) Analyze the data from this experiment (use a = 0.05) and draw conclusions. (18 points) (b) Compute a 95 percent confidence interval estimate of the mean of solution 1. (10 points) (c) Make comparisons among the three washing solutions to determine specifically which solutions differ in the effectiveness of retarding bacterial. (12 points) (d) Construct a set of orthogonal contrasts, assuming that at the outset of the experiment you suspected the effectiveness of solution 2 to be different from the other two. What's your conclusion? (12 points) (e) How would you check whether the basic analysis of variance assumptions satisfied? (5 points) 

QUESTION 8

An experimenter wishes to compare four treatments in blocks of three runs. Develop a balanced incomplete block design for this experiment with four blocks.