Question

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 54 44 35 28 Click here to view the table of critical t-values. LOADING... Click here to view page 1 of the standard normal distribution table. LOADING... Click here to view page 2 of the standard normal distribution table. LOADING... ​(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 -2 -1 0 1 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 negative 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, negative 1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 1.6); (28, 1.1); (30, 0.8); (35, 0.5); (35, 0.3); (37, 0.1); (44, negative 0.1); (44, negative 0.3); (47, negative 0.5); (52, negative 0.8); (54, negative 1.1); (56, negative 1.6). 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 negative 4 to 4 in incrementservals of 1. The graph contains 12 plotted points that follow the general pattern of a line that rises from left to right through (30, negative 2) and (50, 2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, negative 3.3); (28, negative 2.3); (30, negative 1.6); (35, negative 1); (35, negative 0.6); (37, negative 0.2); (44, 0.2); (44, 0.6); (47, 1); (52, 1.6); (54, 2.3); (56, 3.3). All coordinates are approximate. C. 20 30 40 50 60 -2 -1 0 1 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 negative 2 to 2 in incrementstervals 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, negative 1) and (50, 1), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, negative 1.6); (28, negative 1.1); (30, negative 0.8); (35, negative 0.5); (35, negative 0.3); (37, negative 0.1); (44, 0.1); (44, 0.3); (47, 0.5); (52, 0.8); (54, 1.1); (56, 1.6). All coordinates are approximate. D. 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 negative 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, negative 2), with slight deviation from the line pattern at the tails. The 12 plotted points have coordinates as follows: (26, 3.3); (28, 2.3); (30, 1.6); (35, 1); (35, 0.6); (37, 0.2); (44, negative 0.2); (44, negative 0.6); (47, negative 1); (52, negative 1.6); (54, negative 2.3); (56, negative 3.3). All coordinates are approximate. Is it reasonable to conclude that the data come from a population that is normally​ distributed? A. ​Yes, because the plotted values are approximately linear. B. ​No, because the plotted values are not linear. C. ​No, because there are not enough values to make a determination. D. ​Yes, 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, 32.5, 40.5, 49.5, 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, 32.5, 45, 54, 56. 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, 37, 40.5, 49.5, 56. 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, 37, 45, 54, 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. ​Yes, there is at least one point that is greater than the third quartile or less than the first quartile. C. ​Yes, there is at least one point that is outside of the​ 1.5(IQR) boundary. D. ​No, there are no points that are 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 nothing weeks and the upper bound is nothing 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 nothing weeks and the upper bound is nothing weeks. We are 95​% confident that the mean age at which a baby first crawls is within the confidence interval. Click to select and enter your answer(s).

Answer 1

SOLUTION

= Xi / n = 459 / 12 = 38.25

S = sqrt ( Xi² - n² / n-1)

= 10.0011

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

38.25 - 2.201 * 10.0011 / sqrt(12) < < 38.25 + 2.201 * 10.0011 / sqrt(12)

31.8956 < < 44.6044

95% confidence interval for is (31.8956, 44.6044)

We are 95% confident that the mean age at which a baby first crawls is between 31.8956 and 44.6044.