The following data represent the age in weeks at which babie

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,

39, 37, 30, 37

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A) 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 outliers

b) No, the sample contains an outlier

c) No, the population is not normally distributed

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 answers if needed.

a) (____ , ____) (use ascending order. Round to one decimal 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) Nothing can be done

b) Either increase or decrease the sample size

c) Increase the sample size

d) Decrease the sample size

Solution

(A)a) Yes, the population is normally distributed and the sample does not contain outliers

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(B) sample size=n=12

sample mean=39.16667

sample standard deviation =9.073772

The degree of freedom =n-1=12-1=11

Given a=1-0.95=0.05, t(0.025, df=11) =2.2 (from student t table)

So the lower bound is

xbar -t*s/vn =39.16667 -2.2*9.073772/sqrt(12)=33.4

So the upper bound is

xbar +t*s/vn =39.16667 +2.2*9.073772/sqrt(12) =44.9

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(C)c) Increase the sample size