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 |
62 | 41 | 55 | 50 | 47 | 54 | 41 | 63 | 46 |
---|---|---|---|---|---|---|---|---|---|

Sprout Percent |
54 | 67.5 | 63.5 | 67 | 59.5 | 58 | 65.5 | 50.5 | 54 |

- Find the correlation coefficient: r=r= Round to 2 decimal places.
- The null and alternative hypotheses for correlation are:

H0:H0: ? ρ μ r == 0

H1:H1: ? ρ μ r ≠≠ 0

The p-value is: (Round to four decimal places) - Use a level of significance of α=0.05α=0.05 to state the
conclusion of the hypothesis test in the context of the study.
- There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate.
- There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.
- There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful.
- There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds.

- r2r2 = (Round to two decimal places)
- Interpret r2r2 :
- 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 46%.
- There is a 46% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced.
- 46% of all plants produce seeds whose chance of sprouting is the average chance of sprouting.
- Given any group of plants that all produce the same number of seeds, 46% of all of these plants will produce seeds with the same chance of sprouting.

- 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 52 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 0.52 percent.

- 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 52 seeds.

Percent sprouting = (Please round your answer to the nearest whole number.)

Answer #1

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