The data shown to the right represent the age (in weeks) at which babies first crawl, based on a survey of 12 mothers. Complete parts (a) through (c) below.
52
30
44
35
47
37
56
26
39
37
44
44
(a) Draw a normal probability plot to determine if it is reasonable to conclude the data come from a population that is normally distributed. Choose the correct answer below.
A.
20 30 40 50 60
-4 -2 0 2 4
Age (in weeks)
Expected z-score
A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from -4 to 4 in increments of 1. The graph contains 12 plotted points that follow the general pattern of a line that falls from left to right through (30, 2) and (50, -2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 3.3); (30, 2.3); (35, 1.6); (37, 1); (37, 0.6); (39, 0.2); (44, -0.2); (44, -0.6); (44, -1); (47, -1.6); (52, -2.3); (56, -3.3). All coordinates are approximate.
B.
20 30 40 50 60
-4 -2 0 2 4
Age (in weeks)
Expected z-score
A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from -4 to 4 in increments of 1. The graph contains 12 plotted points that follow the general pattern of a line that rises from left to right through (30, -2) and (50, 2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, -3.3); (30, -2.3); (35, -1.6); (37, -1); (37, -0.6); (39, -0.2); (44, 0.2); (44, 0.6); (44, 1); (47, 1.6); (52, 2.3); (56, 3.3). All coordinates are approximate.
C.
20 30 40 50 60
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Age (in weeks)
Expected z-score
A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from -2 to 2 in increments of 0.5. The graph contains 12 plotted points that follow the general pattern of a line that rises from left to right through (30, -1) and (50, 1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, -1.6); (30, -1.1); (35, -0.8); (37, -0.5); (37, -0.3); (39, -0.1); (44, 0.1); (44, 0.3); (44, 0.5); (47, 0.8); (52, 1.1); (56, 1.6). All coordinates are approximate.
D.
20 30 40 50 60
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Age (in weeks)
Expected z-score
A normal probability plot has a horizontal axis labeled "Age (in weeks)" from 20 to 60 in increments of 5 and a vertical axis labeled "Expected z-score" from -2 to 2 in increments of 0.5. The graph contains 12 plotted points that follow the general pattern of a line that falls from left to right through (30, 1) and (50, -1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 1.6); (30, 1.1); (35, 0.8); (37, 0.5); (37, 0.3); (39, 0.1); (44, -0.1); (44, -0.3); (44, -0.5); (47, -0.8); (52, -1.1); (56, -1.6). All coordinates are approximate.
Is it reasonable to conclude that the data come from a population that is normally distributed?
A.
No, because there are not enough values to make a determination.
B.
Yes, because the plotted values are approximately linear.
C.
Yes, because the plotted values are not linear.
D.
No, because the plotted values are not linear.
(b) Draw a boxplot to check for outliers. Choose the correct answer below.
A.
20 30 40 50 60
A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 36, 41.5, 45.5, 56. All values are approximate.
B.
20 30 40 50 60
A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 40, 46, 50, 52. All values are approximate.
C.
20 30 40 50 60
A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 36, 46, 50, 52. All values are approximate.
D.
20 30 40 50 60
A boxplot has a horizontal axis labeled from 20 to 60 in increments of 5. The boxplot has the following five-number summary: 26, 40, 41.5, 45.5, 56. All values are approximate.
Does the boxplot suggest that there are outliers?
A.
No, there are no points that are greater than the third quartile or less than the first quartile.
B.
No, there are no points that are outside of the 1.5(IQR) boundary.
C.
Yes, there is at least one point that is greater than the third quartile or less than the first quartile.
D.
Yes, there is at least one point that is outside of the 1.5(IQR) boundary.
(c) Construct and interpret a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice and fill in the answer boxes to complete your choice. (Round to one decimal place as needed.)
A. The lower bound is ______ weeks and the upper bound is ______ weeks. We are 95% confident that the mean age at which a baby first crawls is outside of the confidence interval.
B. The lower bound is ______ weeks and the upper bound is _____ weeks. We are 95% confident that the mean age at which a baby first crawls is within the confidence interval.