Question

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hyproponics growth procedure that used water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after gemination. Those heights, measured in millimeters, were as follows : 55.5, 60.3, 60.6, 62.1, 65.5, 69.2. Test the claim that the mean tomato plants’heights is different than 65 millimeters. Assume the random sample assumption holds. Use α = 0.05.

(a) State the assumptions.

(b) State hypotheses.

(c) Use t.test() and identify the value of test statistic. Interpret.

(d) Identify the value of p-value.

Answer 1

= (55.5 + 60.3 + 60.6 + 62.1 + 65.5 + 69.2)/6 = 62.2

s = sqrt(((55.5 - 62.2)^2 + (60.3 - 62.2)^2 + (60.6 - 62.2)^2 + (62.1 - 62.2)^2 + (65.5 - 62.2)^2 + (69.2 - 62.2)^2)/5) = 4.71

a) We must assume that the population is normally distributed.

b) H₀: = 65

    H₁: 65

c) The test statistic t = ()/(s/)

                                 = (62.2 - 65)/(4.71/)

                                 = -1.456

df = 6 - 1 = 5

At alpha = 0.05, the critical values are +/- t_{0.025, 5} = +/- 2.571

Since test statistic value is not less than the lower critical value (-1.456 > -2.571), so we should not reject the null hypothesis.

So at 0.05 significance level there is not sufficient evidence to support the claim that the mean tomato plants' height is different than 65 millimeters.

d) P-value = 2 * P(T < -1.456)

                  = 2 * 0.1026

                  = 0.2052