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 68 68 61 49 53 48 59

Sprout Percent 52.8 64.8 58.6 74.4 66.8 74.8 72.4

Find the correlation coefficient: r=r=    Round to 2 decimal places.

The null and alternative hypotheses for correlation are:
H0:H0:      == 0
H1:H1:       ≠≠ 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 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 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 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 61% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced.

61% 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, 61% of all of these plants will produce seeds with the same 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 61%.

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

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	68	68	61	49	53	48	59
Sprout Percent	52.8	64.8	58.6	74.4	66.8	74.8	72.4

Find the correlation coefficient: r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0:      == 0
H1:H1:       ≠≠ 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 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 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 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 61% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced.
- 61% 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, 61% of all of these plants will produce seeds with the same 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 61%.
The equation of the linear regression line is:
ˆyy^ = + xx (Please show your answers to two decimal places)

Accepted Answer

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