Question

A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured. [You may find it useful to reference the t table.]

Fertilizer (ounces)	Height (inches)
1.9	20.4
3.0	49.4
4.3	56.7
1.3	24.3
4.5	29.6
5.3	60.8
3.3	24.6
1.0	25.7
2.6	26
2.4	25.8
0.8	26.2
3.0	28.8
4.3	62.8
3.8	30.1
5.6	43.1
2.6	33.1
4.0	35.2
1.4	22.4
3.5	40.4
6.0	44.2
3.5	29.6
0.5	21.3
1.6	25.7
2.3	29.7
4.6	27.5
3.6	32.5
3.0	33.2
1.0	22.8
2.6	27.3
3.6	46.7

a. Estimate the regression model: Height = β₀ + β₁ Fertilizer + ε. (Round your answers to 2 decimal places.)

Height=____+______Fertilizer

b-1. At the 1% significance level, determine if an ounce of fertilizer increases height by more than 3 units. First, specify the competing hypotheses.

A) H₀: β₁ = 3; H_A: β₁ ≠ 3

B) H₀: β₁ ≤ 3; H_A: β₁ > 3

C) H₀: β₁ ≥ 3; H_A: β₁ < 3

b-2. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test Static=

b-3. Find the p-value.

A) 0.01  p-value < 0.025

B) p-value < 0.01

C) p-value 0.10

D) 0.05  p-value < 0.10

E) 0.025  p-value < 0.05

b-4. At the 1% level of significance, what is the conclusion to the test?

DO NOT REJECT/ REJECT H0, We CAN/ CANNOT conclude an ounce of fertilizer increases hight more then 3 inches

*** Selecr Do not Rejecet or Reject & Select Can or Can not*****

Answer 1

The statistical software output for this problem is :

(a)  Height=17.05+ 5.44 Fertilizer

(b-1)  B) H₀: β₁ ≤ 3; H_A: β₁ > 3

(b-2) Test statistic = 2.163

(b-3)  A) 0.01< p-value < 0.025

(b-4)  DO NOT REJECT H0, We CANNOT conclude an ounce of fertilizer increases hight more then 3 inches