GWU What Does the Anova Table Say About the Null Hypothesis Paper I want you to edit the sentence using your own words. The answer for the following stats questions is correct but I want you to use your own wordings for the sentence. Stat

4.

Problem

Fertilizers A biology student is studying the effect of 10 different fertilizers on the growth of mung bean

sprouts. She sprouts 12 beans in each of 10 different petri dishes, and adds the same amount of fertilizer

to each dish. After one week she measures the heights of the 120 sprouts in millimeters. Here are

boxplots and an

ANOVA table of the data:

Source DF Sum of Squares Mean Square

Fertilizer

9

2073.708

Error

110

21331.083

Total

119

23404.791

230.412

F-Ratio

1.1882

P-Value

0.3097

193.919

a) What are the null and alternative hypotheses?

b) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of heights

and fertilizers).

c) Her lab partner looks at the same data and says that he did t-tests of every fertilizer against every

other fertilizer and finds that several of the fertilizers seem to have significantly higher mean heights.

Does this match your finding in part b? Give an explanation for the difference, if any, between the two

results.

Edit the part below

> Heights=Fertilizers$Heights

> fertlizers=Fertilizers$Fertilizer

> boxplot(Heights~fertlizers)

> summary(throws.AOV)

Df Sum Sq Mean Sq F value Pr(>F)

fertlizers

9

2074

230.4

1.188

0.31

Residuals

110 21331

193.9

A) A null hypothesis is all desired mean bean Hight are the same

Ho : µ1 = µ2 = µ3 … µ10

Alternative hypothesis the mean bean heights are not all equal.

HA : µ2≠ µ2≠ µ3≠……. µ10

B) If P-value is less than the significance level, then reject the null hypothesis

P-value = 0.31 > 0.05 so, we fail to reject Ho(null hypothesis )

So, There is no sufficient evidence to support the claim that at least one of the fertlizers have a

different mean height.

C) Since we do not reject our null hypothesis, we can conclude that there is no evidence to provide

the mean beans height are differ. In this case t-tests of every fertilizer against every other fertilizer

and finds that several of the fertilizers seem of have significantly higher mean height. The difference

is due to the probability of a type I error being much larger when combining the result of many

hypothesis tests.

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