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myopenmath.com 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 50 67 58 52 41 68 60 48 Sprout Percent 46 68 56.5 63 61 62.5 50 57 63 a. Find the correlation coefficient: r = (Round to three decimal places.) b. The null and alternative hypotheses for correlation are: Ho: 7 v =0 H1: 2 0 c. The p-value is: (Round to three decimal places) d. Use a level of significance of a = 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 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. 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. e. 72 = (Round to three decimal places) f. Interpret 72 : Given any group of plants that all produce the same number of seeds, 50% 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 50%. 50% of all plants produce seeds whose chance of sprouting is the average chance of sprouting. There is a 50% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced. 9. The equation of the linear regression line is: y = + (Please show your answers to three decimal places) h. Use the model to predict the percent of seeds that sprout if the plant produces 53 seeds. Percent sprouting = (Please round your answer to the nearest whole number.) i. 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 0.543 percent. j. Interpret the y-intercept in the context of the question: The average sprouting percent is predicted to be 89.075. The best prediction for a plant that has 0 seeds is 89.075 percent. If plant produces no seeds, then that plant's sprout rate will be 89.075. @ # % Be k 2 6 8 9
