Suppose a recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.4 ft. A

biologist observing a huge field of mature plants of this particular species of sunflower thinks that the mean height is shorter

than reported. He measures the heights of 45 randomly selected sunflowers and finds the mean height to be 10.1 ft.

The hypotheses of interest are:

(A) H0 : µ = 10.1 vs Ha : µ < 10.1

(B) H0 : µ > 10.4 vs Ha : µ = 10.4

(C) H0 : ¯x = 10.1 vs Ha : ¯x > 10.1

(D) H0 : ¯x = 10.1 vs Ha : ¯x < 10.1

(E) H0 : µ = 10.4 vs Ha : µ < 10.4

Answer: (E) H0 : µ = 10.4 vs Ha : µ < 10.4

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

From the given situation,

The recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.4 ft. This is the null hypothesis.

The biologist sunflower thinks that the mean height is shorter than reported. This is the alternative hypothesis.

Therefore, the correct null and alternative hypotheses are

(E) H0 : µ = 10.4 vs Ha : µ < 10.4