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	19	30	29	19	18	28	31	31	18	26	23	28	29	24	28	20	34	28	32	34	35

(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 90% 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 57. (Give your answers correct to one decimal place.)

Lower Limit
Upper Limit

Answer 1

Here is the R code: