# Hypothesis

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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?

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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