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	54	53	62	66	50	41	40
Sprout Percent	61	59.5	50	55	69	73.5	72

1. Find the correlation coefficient: r=r=   Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ?ρμr == 0
   H1:H1: ?rρμ ≠≠ 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 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.
   • 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 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 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.
4. r2r2 = (Round to two decimal places)
5. The equation of the linear regression line is:   
   ˆyy^ = + xx   (Please show your answers to two decimal places)
   
6. Use the model to predict the percent of seeds that sprout if the plant produces 57 seeds.
   Percent sprouting = (Please round your answer to the nearest whole number.)

Answer 1