Self Test 9 for Probability and Statistics

Analysis of Variance

This test was constructed by Zauresh Atakhanova based on the Schaum's Outline Theory and Problems of Probability and Statistics by Murray R. Spiegel. If you need more review refer also to this outline.

One-way classification or one-factor experiments

1. True False.Table 1 shows the price in dollars of a certain stock under three possible scenarios.

 A 38 39 40 39 B 37 39 38 38 C 39 41 40 40

(a) the mean price for different scenarios, (b) the grand mean for all scenarios, (c) the total variation, (d) the variation between scenarios and (e) the variation within scenarios. Use the long method.

Are:

a)      39, 38, 40

b)      39

c)      14

d)      8

e)      6

2. True False.Referring to Problem 1 find an unbiased estimate of the population variance s2 from (a) the variation between scenarios under the null hypothesis of equal scenario means, and (b) the variation within scenarios.

Are:

a)      4.5

b)      0.8

## Modifications for unequal numbers of observations

3. True False.Referring to Problem 1, can we reject the null hypothesis of equal means at (a) 0.05 significance level, (b) 0.01 significance level?

4. True False.Table 3 shows the lifetimes in hours of samples from the three different types of light bulbs manufactured by a company. Using the long method, test at (a) the 0.05, and (b) the 0.01 significance level whether there is a difference in the three types.

(a)    no difference

(b)   no difference

Two-way classification or two-factor experiments

5. True False. The following table shows productivities of three different machines making four different products. Using the long method, test at 1% level of significance whether (a) there isn't a significant difference in the productivity per hour due to type of machine and, (b) there is a significant difference in productivity per hour due to the type of the product.

 Product 1 Product 2 Product 3 Product 4 Machine A 4.5 6.4 7.2 6.7 Machine B 8.8 7.8 9.6 7.0 Machine C 5.9 6.8 5.7 5.2