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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
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 42, 42, 68, 48, 59, 69, 40, 67
- Sprout Percent 63.2,69.2,56.8,50.8,47.4, 45.4, 71, 44.2
- Find the correlation coefficient:r= Round to 2 decimal places.
- The null and alternative hypotheses for correlation are:
- The p-value is:(Round to four decimal places)
- Use a level of significance of=0.05to 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 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 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.
- r2=(Round to two decimal places)
- Interpretr2:
- 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 65%.
- 65% 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, 65% of all of these plants will produce seeds with the same chance of sprouting.
- There is a 65% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced.
- The equation of the linear regression line is:y^=+x(Please show your answers to two decimal places)
- Use the model to predict the percent of seeds that sprout if the plant produces 60 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:
- 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 0.68 percent.
- 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.
- Interpret the y-intercept in the context of the question:
- If plant produces no seeds, then that plant's sprout rate will be 92.82.
- The best prediction for a plant that has 0 seeds is 92.82 percent.
- The y-intercept has no practical meaning for this study.
- The average sprouting percent is predicted to be 92.82.
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