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 Sprout Percent 65 57 55 70 58 63.8 59 61.4 40 77 69 58.4 66 60.6 45 66 47 58.2 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: H: ? = 0 H: ? #0 The p-value is: (Round to four decimal places) c. 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 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 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 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. (Round to two decimal places) e. Interpretra: Given any group of plants that all produce the same number of seeds, 47% of all of these plants will produce seeds with the same chance of sprouting. There is a 47% chance that the regression line will be a good predictor for the percent of seeds that sprout based on the number of seeds produced. 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 47%. 47% of all plants produce seeds whose chance of sprouting is the average chance of sprouting. 1. The equation of the linear regression line is: (Please show your answers to two decimal places) g. Use the model to predict the percent of seeds that sprout if the plant produces 56 seeds. Percent sprouting (Please round your answer to the nearest whole number.) d. p2

Answer 1

(a) r = -0.68

(b) H₀: $\rho$ = 0

H_a: $\rho$ ≠ 0

p-value = 0.0420

(c) Option B

(d) r2 = 0.47

(e) Option C

(f) y = 88.25 - 0.44*x

(g) 64

(h) Option B

(i) Option B

	r²	0.47
	r	-0.68
	Std. Error	5.080
	n	9
	k	1
	Dep. Var.	Percent
ANOVA table
Source	SS	df	MS	F	p-value
Regression	159.2448	1	159.2448	6.17	.0420
Residual	180.6752	7	25.8107
Total	339.9200	8
Regression output				confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper
Intercept	88.25
Produced	-0.44	0.1772	-2.484	.0420	-0.8592	-0.0211