# Hypothesis

The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky substance and then examining the insects trapped on the board. To investigate which colors are the most attractive to cereal leaf beetles, researchers place six boards of each of four colors in a field of oats. The table below gives data on the number of cereal leaf beetles trapped.

Color Insects Trapped

Yellow 45 59 48 46 38 47

White 21 12 14 17 13 17

Green 37 32 15 25 39 41

Blue 16 11 20 21 14 7

Test the hypothesis that the color of the board has no effect in attracting cereal leaf beetles at  = 0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colors.

a. Define the null alternative hypothesis.

b. Define the alternate hypothesis.

c. Let  = 0.05. Determine the rejection region.

d. Compute the test statistic.

e. What is the conclusion?

Test the hypothesis that the color of the board has no effect in attracting cereal leaf beetles at  = 0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colors.

a.Define the null alternative hypothesis.

b.Define the alternate hypothesis.

c.Let  = 0.05. Determine the rejection region.

d.Compute the test statistic.

e.What is the conclusion?

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#### Solution Summary

The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky substance and then examining the insects trapped on the board. To investigate which colors are the most attractive to cereal leaf beetles, researchers place six boards of each of four colors in a field of oats. The table below gives data on the number of cereal leaf beetles trapped.

Color Insects Trapped

Yellow 45 59 48 46 38 47

White 21 12 14 17 13 17

Green 37 32 15 25 39 41

Blue 16 11 20 21 14 7

Test the hypothesis that the color of the board has no effect in attracting cereal leaf beetles at  = 0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colors.

a. Define the null alternative hypothesis.

b. Define the alternate hypothesis.

c. Let  = 0.05. Determine the rejection region.

d. Compute the test statistic.

e. What is the conclusion?