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?

THIS HAS BEEN ANSWERED ONCE, BUT A LITTLE BIT OF EXPLANATION FOR B), F), AND G)?

Answer 1

Answers to (b), (f) and (g) are asked.

(b)

We shall use a t - interval to construct a 90% confidence interval. Reason: Sample Size = n = 12 < 30. Small Sample. So, Central Limit Theorem cannot be applied. Also Population Standard deviation is not provided and it has to be estimated from sample standard deviation.

(f)

The 90% confidence interval that we constructed for the mean age at which a baby first crawls gives a range of values that is likely to contain an unknown population mean mean age at which a baby first crawls.

If the experiment is repeated a large number of times and in each experiment the confidence interval for mean mean age at which a baby first crawls.is calculated, then 90% of these confidence intervals will contain the population mean mean age at which a baby first crawls.

(g)

Accuracy of the confidence interval can be increased by:

(i) Increase the sample size. A bigger sample gives more information about the population and allows us to make a precise estimate.

(ii) Decrease the standard deviation. A smaller standard deviation indicates the data are more precise and less spread.

(h)

From Table, for = 0.10, Z = 1.645.

= 10

e = 3

Substituting , we get n = 31