Exercise 9 A researcher studies the effect of ten distinct fertilizers on the gr

Question

Exercise 9 A researcher studies the effect of ten distinct fertilizers on the growth of a plant. He sprouts twelve seeds in each of 10 different Petri dishes containing the different fertilizers, with the exact same quantity of fertilizer in each dish. After three days, he measures the height of the 120 plants, and gets the following boxplots and ANOVA output: 140 Df Sum Sq Mean Sq F value Pr(>F) 100 Fertilizer 9 2073.7 230.4 1.18 0.3097 Residuals 110 213311 193.9 60 50 A B CD EF G H Fertiizer 1. What are Ho and HA? 2. What does the ANOVA output say about this testing problem? 3. Do the assumptions for the test seem to be reasonable? Explain 4. His colleague analyses the same data by doing a t-test of every fertilizer against every other fertilizer. He finds that several of the fertilizers against every other fertilizer and finds that several of them have significantly higher mean heights. Does this match your finding of question 2? Give an explanation for the difference, if any, between the two re- anlls

Explanation / Answer

1. H0 and HA are

H0: The mean height of plant are same for all fertilizers.

HA: The mean height of plant are not same for all fertilizers.

2. ANOVA Output

The p-value is 0.3097 > significance level 5%.

So, looking the p-value we fail to reject the null hypothesis.

So we can conclude that, the mean height of plant are not same for all fertilizers.

3. Assumptions for ANOVA

* The Sample (height of plant of all fertilizers) are independent

* The response variable (height of plant) is approximately normally distributed

* The population variances are equal across responses for the group levels

4. In ANOVA, if we want to compare more than two groups we use ANOVA and

In t test, if want to compare only two groups we use t test.

If we want to check is there any group is significant in ANOVA then we use post hoc test by seeing p-value. But in our result p-value is > significance level so, we fail to reject null hypothesis.

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