Suppose a recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.1 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 35 randomly selected sunflowers and finds the mean height to be 9.6 ft. Select the correct null, H 0 , and alternative, H 1 , hypotheses.

Null hypothesis:  

Alternative hypothesis:  

Or equivalently :

Null hypothesis:  

Alternative hypothesis:  

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the sample standard deviation for the sample  

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 10.1 ft (alternative hypothesis) , then the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Or equivalently :

Null hypothesis:  

Alternative hypothesis:  

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

4

step-by-step explanation: