Question

Twenty-one mature flowers of a particular species were dissected, and the number of stamens and carpels present in each flower were counted.

x, Stamens	52	68	70	38	61	51	56	65	43	37	36	74	38	35	45	72	59	60	73	76	68
y, Carpels	21	30	29	19	20	30	31	31	18	26	23	28	29	24	28	20	34	28	34	36	33

(a) Is there sufficient evidence to claim a linear relationship between these two variables at α = .05?
(i) Find r. (Give your answer correct to three decimal places.)

(iii) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence to claim a linear relationship. Reject the null hypothesis, there is significant evidence to claim a linear relationship.     Fail to reject the null hypothesis, there is significant evidence to claim a linear relationship. Fail to reject the null hypothesis, there is not significant evidence to claim a linear relationship.

(b) What is the relationship between the number of stamens and the number of carpels in this variety of flower?. (Give your answers correct to two decimal places.)

=

+ x

(c) Is the slope of the regression line significant at α = .05?(i) Find t. (Give your answer correct to two decimal places.)


(ii) Find the P-value. (Give your answer bounds exactly.)
< p <
(iii) State the appropriate conclusion.

Reject the null hypothesis, there is not evidence of a significant slope. Reject the null hypothesis, there is evidence of a significant slope.     Fail to reject the null hypothesis, there is evidence of a significant slope. Fail to reject the null hypothesis, there is not evidence of a significant slope.

(d) Find the 99% prediction interval for the number of carpels that one would expect to find in a mature flower of this variety if the number of stamens were 59. (Give your answers correct to one decimal place.)

Lower Limit
Upper Limit

Answer 1

Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel output is given below:

Regression Analysis
Regression Statistics
Multiple R	0.489677231
R Square	0.239783791
Adjusted R Square	0.199772411
Standard Error	4.816531829
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	1	139.0289254	139.0289254	5.992889871	0.024248198
Residual	19	440.7805984	23.19897886
Total	20	579.8095238
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	16.87279181	4.3626304	3.867573061	0.001036819	7.741701461	26.00388216
x, Stamens	0.184937444	0.07554517	2.448037963	0.024248198	0.026819586	0.343055302
For Individual Response Y
Interval Half Width	14.11848419
Prediction Interval Lower Limit	13.66561684
Prediction Interval Upper Limit	41.90258522

(a) Is there sufficient evidence to claim a linear relationship between these two variables at α = .05?
(i) Find r. (Give your answer correct to three decimal places.)

Answer:

(iii) State the appropriate conclusion.

Answer: Reject the null hypothesis, there is significant evidence to claim a linear relationship.

Explanation: Because the p-value for the slope coefficient is less than the significance level 0.05

(b) What is the relationship between the number of stamens and the number of carpels in this variety of flower?. (Give your answers correct to two decimal places.)

Answer:

(c) Is the slope of the regression line significant at α = .05?(i) Find t. (Give your answer correct to two decimal places.)

(ii) Find the P-value. (Give your answer bounds exactly.)
0.01< p < 0.05
(iii) State the appropriate conclusion.

Answer: Reject the null hypothesis, there is evidence of a significant slope.


(d) Find the 99% prediction interval for the number of carpels that one would expect to find in a mature flower of this variety if the number of stamens was 59. (Give your answers correct to one decimal place.)

Lower Limit	13.7
Upper Limit	41.9