The data to the right represents the age in weeks at which b

The data to the right represents the age (in weeks) at which babies first crawl based on a survey of 12 mothers. 52 30 44 35 47 37 56 26 35 47 30 28

Mean = 38.92

Standard deviation=10

A.) Because the sample size is small, we must verify that the data come from a population that is normally distributed & 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 & sample doesn’t contain outliers.

b. No, population is not normally distributed

c. No, 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 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.) Because the sample size is small, we must verify that the data come from a population that is normally distributed & 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 & sample doesn’t contain outliers.

B)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    38.91666667          
t(alpha/2) = critical t for the confidence interval =    2.20098516          
s = sample standard deviation =    9.995074545          
n = sample size =    12          
df = n - 1 =    11          
Thus,              
              
Lower bound =    32.56609928          
Upper bound =    45.26723405          
              
Thus, the confidence interval is              
              
(   32.56609928   ,   45.26723405   ) [ANSWER]

c)

What could be done to increase the accuracy of the interval without changing the level of confidence?
c) Increase the sample size [ANSWER]