Exercises. 1. An anova was performed and the following partially completed anova table is available:

1. An ANOVA was performed and the following partially completed ANOVA table is available:

Source of Sum of Degrees of Mean variation squares freedom squares	F ratios
Between groups 7 26 Within blocks 14 Error 57.900 Total 402.100

a) Complete the analysis of variance table.

b) How many populations are being tested?

c) How many blocks were used in this analysis of variance?

d) Using an alpha equal to 0.05, test the null hypothesis that the population means are equal for all groups.

e) Using an alpha equal to 0.05, test the null hypothesis that the population means are equal for all blocks.

2. Three analysts were asked to predict earnings growth over the coming year for four companies producing cars. Their forecasts (in percentage increase in earnings) are given below

Analysts Cars companies

A B C D

1 7 11 10 13 2 8 9 13 12 3 9 13 16 15

a) Set out analysis of variance table

b) For test the null hypothesis that the population mean growth forecasts are the same for all car companies.

c) For test the null hypothesis that the population mean growth forecasts are the same for all analysts.

3. A soft drink producer wants to compare the effects on sales of can colors: red, yellow, and blue. He selects four regions and in three stores in each region, each to sell one color cans. The following table shows number of sales (in hundreds of cans) at the end of the experiment.

Regions Can colors

Red Yellow Blue

Region I 37 28 25 Region II 29 33 22 Region III 31 29 27 Region IV 23 26 26

a) Set out analysis of variance table

b) Test the null hypothesis that the population mean sales are the same for each can color. Use p- value approach.

c) Test the null hypothesis that the population mean sales are the same for all four regions. Use p- value approach.

4. Three real estate agents were each asked to assess the values of five houses. The results, in thousands of dollars, are shown below.

House Agents

A B C

I 200 210 220 II 190 192 196 III 180 195 205 IV 160 182 194 V 170 171 185

a) Set out analysis of variance table.

b) Test at 5% significance level the null hypothesis that population mean valuations are the same for the three real estate agents.

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