Suppose you want to determine whether the brand of laundry d

Suppose you want to determine whether the brand of laundry detergent and the wash temperature affects the amount of dirt removed from your laundry. You buy two different brands of detergent:

Solution

Null hypothesis: Factor A is not significant.

Alternative hypothesis: Factor A is signficant.

The test statistic is

F=1.11

Given a=0.01, the critical value is F(0.99, df=1, df2=36) =7.40 (from F table)

The rejection region is if F>7.40, we reject the null hypothesis.

Since F=1.11 is less than 7.40, we do not reject the null hypothesis.

So we can not conclude that Factor A is signficant.

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Null hypothesis: Factor B is not significant.

Alternative hypothesis: Factor B is signficant.

The test statistic is

F=19.55

Given a=0.01, the critical value is F(0.99, df=1, df2=36) =7.40 (from F table)

The rejection region is if F>7.40, we reject the null hypothesis.

Since F=19.55 is larger than 7.40, we do reject the null hypothesis.

So we can conclude that Factor B is signficant.

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Null hypothesis: interaction AxB is not significant.

Alternative hypothesis: interaction AxB is signficant.

The test statistic is

F=0.04

Given a=0.01, the critical value is F(0.99, df=1, df2=36) =7.40 (from F table)

The rejection region is if F>7.40, we reject the null hypothesis.

Since F=0.04 is less than 7.40, we do reject the null hypothesis.

So we can not conclude that interaction AxB is signficant.