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...

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.

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


2. The null and alternative hypotheses for correlation are:
   H0:H0:      == 0
   H1:H1:       ≠≠ 0
   The p-value is:    (Round to four decimal places)
   
   
   
   


3. 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.
   
   

   
   
   
   


4.  r2r2 =  (Round to two decimal places)


5.  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%.
   
   

   
   
   
   


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