Researchers believe that plants growing at different altitudes grow to different

Question

Researchers believe that plants growing at different altitudes grow to different heights. They examine one type of plant at low, medium-low, medium, medium-high, and high altitudes, measuring their heights in cm. In each altitude group, they have a sample of 25 plants. a. Write the null and alternative hypothesis for the ANOVA test. Ho: Ha Instead of an ANOVA test, could a Chi-Squared Goodness of Fit test be conducted? Why or why not? b. What assumptions must be true in order to perform the ANOVA test? Circle all that are true. c. The heights of each plant must be independent. There must be at least 20 plants in each group, no matter if the distribution of heights is normal or not. The variances of height must be the same at each altitude in the population. i. ii. iii.

Explanation / Answer

a. H0 : Mean height of all the plants at different altitudes are same.

Ha : At least at one altitude mean height of plants are different from the other group

b. A chi-square test for independence can be employed here so check that heights are independnt or not with the altitudes but the goodness of fit test are not relevant herre.

c. (i) heightss must be independent. YES

(ii) No, the second assumption is irrelevant

(iii) Yes, equality of varianceis an assumption.

d.

(e) Here as the p - value is less than 0.05 so we can reject the null hypothesis and can conclude that plant heights are different at diffeent altitudes.  

ANOVA Source of Variation SS df MS F P-value Between Groups 1874 4 468.5 3.390832 0.009 Within Groups 16580 120 138.16667 Total 18454 124

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