Exercises. 1. The following ANOVA table, based on information obtained for four samples selected from four independent populations that are normally distributed with

1. The following ANOVA table, based on information obtained for four samples selected from four independent populations that are normally distributed with equal variances, has a few missing values

Source of Sum of Degrees of Mean variation squares freedom squares	F ratio
Between groups Within groups 168.245 Total 19

a) Complete the analysis of variance table.

b) Using , test the null hypothesis that the means of the four populations are equal against the alternative hypothesis that the means of the four populations are not equal.

2. Respond to each of the following questions using this partially completed one-way ANOVA table

Source of Sum of Degrees of Mean variation squares freedom squares	F ratio
Between groups 3 Within groups 405 Total 888 31

a) How many different populations are being considered in this analysis?

b) Fill in the ANOVA table with missing values.

c) State the appropriate null and alternative hypothesis.

d) What conclusions should be reached regarding the null hypothesis?

Test using an .

3. Three samples randomly selected from three independent populations that are normally distributed with equal variances produced the following data.

Sample I	Sample II	Sample III

a) Set out the analysis of variance table for these data.

b) Test at a 1% significance level, the null hypothesis that the means of these three populations are equal.

4. Consider the following data obtained for two samples selected at random from two populations that are independent and normally distributed with equal variances

Sample I	Sample II

a) Set out the analysis of variance table for these data.

b) Test at a 5% significance level, the null hypothesis that the means of these three populations are equal.

5. A company hired three new salespersons with degrees in mathematics, economics and marketing. The company wants to check if the fields of study have any effect on the mean number of sales made by these salespersons. The following table lists the number of items sold by these three salespersons during certain randomly selected days.

Person with Math. degree	Person with economics degree	Person with marketing degree

a) Set out the analysis of variance table for these data.

b) Using the 5% significance level, can you reject the null hypothesis that the mean number of items sold per day by all salespersons with degrees in each of these three areas is the same?

6. A consumer agency that wanted to compare drying times for paints made by three companies tested a few samples of paints from each of these companies. The following table lists the drying times (in minutes) for these samples of paints

Company A	Company B	Company C

a) Set out the analysis of variance table for these data.

b) Using the 1% significance level, test the null hypothesis that the mean drying times for paints of these companies are equal.

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