A student wanted to study the effects of a new type of plant food on the growth of a particular type of flower. Using five different concentrations of food, the plants were then allowed to grow over a 2-month period. At the end of the 2 months, the heights of the plants were measured. A regression analysis was completed, and the relationship was found to be linear with the least squares equation of ŷ = 3.31 + 1.37x, where y is the height of the plant and x is the concentration of the plant food. The standard error for the slope was found to be 0.39. (a) Calculate the test statistic for a hypothesis test for the slope. (Round your answer to two decimal places.) (b) A hypothesis test was done for the slope of the least squares regression line, and a P-value of 0.0056 was found. Which of the following conclusions is appropriate? (Use ? = 0.05.) Fail to reject the null hypothesis and conclude that there is sufficient evidence of a linear relationship between the concentration of food and the height of the plant.Fail to reject the null hypothesis and conclude that there is insufficient evidence of a linear relationship between the concentration of food and the height of the plant. Reject the null hypothesis and conclude that there is insufficient evidence of a linear relationship between the concentration of food and the height of the plant.Reject the null hypothesis and conclude that there is sufficient evidence of a linear relationship between the concentration of food and the height of the plant.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A student wanted to study the effects of a new type of plant food on the growth of a particular type of flower. Using five different concentrations of food, the plants were then allowed to grow over a 2-month period. At the end of the 2 months, the heights of the plants were measured. A regression analysis was completed, and the relationship was found to be linear with the least squares equation of

ŷ = 3.31 + 1.37x,

where y is the height of the plant and x is the concentration of the plant food. The standard error for the slope was found to be 0.39.

(a)

Calculate the test statistic for a hypothesis test for the slope. (Round your answer to two decimal places.)

(b)

A hypothesis test was done for the slope of the least squares regression line, and a P-value of 0.0056 was found. Which of the following conclusions is appropriate? (Use

? = 0.05.)

Fail to reject the null hypothesis and conclude that there is sufficient evidence of a linear relationship between the concentration of food and the height of the plant.Fail to reject the null hypothesis and conclude that there is insufficient evidence of a linear relationship between the concentration of food and the height of the plant. Reject the null hypothesis and conclude that there is insufficient evidence of a linear relationship between the concentration of food and the height of the plant.Reject the null hypothesis and conclude that there is sufficient evidence of a linear relationship between the concentration of food and the height of the plant.

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