Answered: A biologist looked at the relationship…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 55SE: Use the following scenario for the exercises that follow: In the game of Keno, a player starts by...

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Question

A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below.

Seeds Produced	60	49	49	41	58	56	50	52
Sprout Percent	61	73.3	82.3	79.7	63.6	69.2	84	71.4

r2 = (Round to two decimal places)

Interpret r2r2 :

Given any group of plants that all produce the same number of seeds, 66% of all of these plants will produce seeds with the same chance of sprouting.
There is a 66% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced.
66% of all plants produce seeds whose chance of sprouting is the average chance of sprouting.
There is a large variation in the percent of seeds that sprout, but if you only look at plants that produce a fixed number of seeds, this variation on average is reduced by 66%.

The equation of the linear regression line is:
ˆyy^ = + xx (Please show your answers to two decimal places)

Use the model to predict the percent of seeds that sprout if the plant produces 51 seeds.
Percent sprouting = (Please round your answer to the nearest whole number.)

Interpret the slope of the regression line in the context of the question:

The slope has no practical meaning since it makes no sense to look at the percent of the seeds that sprout since you cannot have a negative number.
As x goes up, y goes down.
For every additional seed that a plant produces, the chance for each of the seeds to sprout tends to decrease by 1.13 percent.

Interpret the y-intercept in the context of the question:

The best prediction for a plant that has 0 seeds is 131.58 percent.
The average sprouting percent is predicted to be 131.58.
The y-intercept has no practical meaning for this study.
If plant produces no seeds, then that plant's sprout rate will be 131.58.

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