Question

In: Statistics and Probability

Twenty-one mature flowers of a particular species were dissected, and the number of stamens and carpels...

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

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