Question

The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers conducted by Essential Baby. Crawling ages (in weeks) are known to be normally distributed.

52 30 44 35 39 26 47 37 56 25 39 28

Please include the letter each part below as you answer the following questions.

a) What is the point estimate for the population mean number of weeks babies first crawl?

b) Shall we use a z-interval or a t-interval to construct a 90% confidence interval? Why? (You will need to answer this part questions with a complete sentence or two.)

c) What is the critical value for this confidence interval?

d) Construct a 90% confidence interval for the mean age at which a baby first crawls.

e) What is the margin of error for this confidence interval?

f) Interpret the 90% confidence interval that you constructed for the mean age at which a baby first crawls in terms of repetitions of collecting samples. (You will need to answer this part with a complete sentence or two.)

g) What can be done to increase the accuracy of the interval without changing the level of confidence? (You will need to answer this question with a complete sentence or two.

h) Suppose the population standard deviation of the age at which babies first crawl was known to be 10 months. What sample size would be needed to have a margin of error of only 3 months?

Answer 1

a) What is the point estimate for the population mean number of weeks babies first crawl?

point estimate=sample mean=xbar=sum/total=458/12=38.16667

b) Shall we use a z-interval or a t-interval to construct a 90% confidence interval? Why? (You will need to answer this part questions with a complete sentence or two.)

t interval since sample size here n=12 that is n<30 and population standard deviation is not given.

c) What is the critical value for this confidence interval?

df=n-1=12-1=11

alpha=0.10

alpha/2=0.10/2=0.05

t crit for alpha/2 and 11df is

=T.INV(0.05;11)

=1.79588

d) Construct a 90% confidence interval for the mean age at which a baby first crawls.

xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)

38.16667-1.79588*10.11599/sqrt(12),38.16667+1.79588*10.11599/sqrt(12)

32.92,43.41

90% lower limit for mean=32.92

90% upper limit for mean=43.41

e) What is the margin of error for this confidence interval?

margin of error =tc*s/sqrt(n

=1.79588*10.11599/sqrt(12)

=5.244391

Solutionf:

we are 90% confident that the true popualtion mean age (in weeks) at which babies first crawl lies in between

32.92 and 43.41 weeks