11.14 To study the effect of the type of soil on the amount of growth attained by a new hybrid plant, saplings were planted in three different types of soil and their subsequent amounts of growth classified into three categories:

Soil Type Growth Clay Sand Loam Poor 16 8 14 Average 31 16 21 Good 18 36 25 Total 65 60 60 Does the quality of growth appear to be distributed differently for the tested soil types at the 0.05 level?

a. State the null and alternative hypotheses.

b. Find the expected value for the cell containing 36.

c. Calculate the value of chi-square for these data.

d. Find the p-value.

e. Find the test criteria [level of significance, test statistic, its distribution, critical region, and critical value(s)].

f. State the decision and the conclusion for this hypothesis test.

Part III: Understanding the Concepts