a.
Is there a linear association between mammals’ gestation and longevity? Explain your answer completely. Use a scatterplot and the
correlation coefficient
to justify your answer.
Yes, there is a linear association between mammals gestion and longevity. Both variables increase and decrease together creating a moderate positive linear association.
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 53.063642 + 10.414122 x Equation for least squares line
Sample size: 40
R (correlation coefficient) = 0.59142509
R-sq = 0.34978364
Estimate of error standard deviation: 119.15027
Parameter estimates:
Parameter
|
Estimate
|
Std. Err.
|
Alternative
|
DF
|
T-Stat
|
P-value
|
Intercept
|
53.063642
|
36.455574
|
≠ 0
|
38
|
1.4555701
|
0.1537
|
Slope
|
10.414122
|
2.3033508
|
≠ 0
|
38
|
4.5212924
|
|
Analysis of variance table for regression model:
Source
|
DF
|
SS
|
MS
|
F-stat
|
P-value
|
Model
|
1
|
290211.91
|
290211.91
|
20.442085
|
|
Error
|
38
|
539477.87
|
14196.786
| | |
Total
|
39
|
829689.77
| | | |
b. Use technology to find the equation for the least squares line for predicting a mammal's gestation period (y) from its longevity (x).
53.063642 + 10.414122x
53.064 + 10.414x
c. Use the least squares line to calculate the predicted gestation for a baboon.
53.064 + 10.414 (20)= 261.344
Use x value for Baboon.
d. Calculate the residual value for the gestation of a baboon, and state whether you overpredicted or underpredicted the gestation for a baboon in part (c).
Residual is y-= 187-261.344= -74.344 Under predicted below the residual line.
0
e. Use the original least squares line to predict the gestation period of a human being, assuming a longevity of 75 years.
53.064 + 10.414 (75)=834.114
f. Why does your answer for part (e) differ so much from the average gestation period of a human (280 days)?
My answer differs because some animals have a longer gestation time than human
280-834.114=-554.114
A biologist believes that the gestation period for a mouse is not 21 days, as reported. She decides to randomly select 35 mice and record their gestation times, in days. The results are given in the following table:
22
|
22
|
20
|
19
|
20
|
23
|
24
|
20
|
24
|
20
|
20
|
24
|
23
|
23
|
21
|
22
|
20
|
22
|
23
|
21
|
22
|
23
|
21
|
20
|
21
|
22
|
24
|
21
|
24
|
21
|
22
|
|
g. Is there evidence to suggest that the average gestation period for a mouse is different from 21 days? Use Be sure to complete all of the necessary steps of the hypothesis test. No need to show work for calculations.
One sample proportion hypothesis test:
Outcomes in : var1
Success : 21
p : Proportion of successes
H0: p = 0.05
HA: p ≠ 0.05
Hypothesis test results:
Variable
|
Count
|
Total
|
Sample Prop.
|
Std. Err.
|
Z-Stat
|
P-value
|
var1
|
7
|
31
|
0.22580645
|
0.039144068
|
4.4912668
|
|
We have enough evidence to reject the Null Hypothesis. There is sufficient evidence that the average gestation period for a mouse is different than 21 days.
h. Estimate the average gestation period of a mouse using a 95% confidence interval, and interpret your answer.
One sample proportion confidence interval:
Outcomes in : var1
Success : 21
p : Proportion of successes
Method: Standard-Wald
95% confidence interval results:
Variable
|
Count
|
Total
|
Sample Prop.
|
Std. Err.
|
L. Limit
|
U. Limit
|
var1
|
7
|
31
|
0.22580645
|
0.075095186
|
0.078622591
|
0.37299031
|
The average gestation period of a mouse using a 95% confidence interval is between 0.079 and 0.373.