The following data represent the age (in weeks) at which babies first crawl base
ID: 3170222 • Letter: T
Question
The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers.
52
30
44
35
47
37
56
26
44
39
44
26
Mean=40.0
StDev=9.65
Because the sample size is small, we must verify that the data come from a population that is normally distributed and that the sample size does not contain any outliers. Are the conditions for constructing a confidence interval about the mean satisfied?
A.Yes, the population is normally distributed and the sample does not contain any outliers.
B.No, the population is not normally distributed.
C.No, the sample contains an outlier.
(b) Construct a 95% confidence interval for the mean age at which a baby first crawls. Select the correct choice below and fill in any answer boxes in your choice.
A.(____,____)
(Use ascending order. Round to one decimal place as needed.)
B.A 95%confidence interval cannot be constructed.
(c) What could be done to increase the accuracy of the interval without changing the level of confidence?
A.Decrease the sample size.
B.Either increase or decrease the sample size.
C.Increase the sample size.
D.Nothing can be done.
52
30
44
35
47
37
56
26
44
39
44
26
A normal probability plot with bounds governed by two curves has a horizontal axis labeled "Age (in weeks)" from 0 to 60 in increments of 10 and a vertical axis labeled "Percent" from 1 to 99 with intermediate tick marks labeled 25, 50, and 75. The outer vertical tick marks are farther apart from each other than the inner vertical tick marks. There is a line, rising from left to right, which passes through the points (27, 25) and (53, 75). Twelve plotted points generally follow the pattern of the line. All of the points are between the bounds. All coordinates are approximate.A horizontal boxplot has a number line labeled from less than 30 to 60 in increments of 5 and consists of a box extending from 30 to 48 with a vertical line through the box at 44 and two horizontal lines extending from the left and right sides of the box to 26 and 56, respectively. All values are approximate.
Explanation / Answer
No, population is not normally distributed.
so for finding confidence interval we use t distribution .
formula of confidence inteval is
( xbar - E ,xbar +E)
where E =tc * s/sqrt (n)
here given , xbar = 40 , s =9.65 ,n =12
tc for 95% confidence level with df = n -1 = 11 is 2.201
tc=2.201
plug all values in formula of E
you get E = 6.13
confidence interval is
( 40- 6.13 , 40+ 6.13)
( 33.87 , 46.13)
( 33.9 , 46.1) this is the 95% confidence interval.
C)
If you increase the sample size then accuracy of confidence interval is increase.
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