Question

# Confidence Intervals for proportions generally require a large sample. However, there are corrections to the

formula that allow us to give point estimates for the means of smaller samples, i.e., if np<5, n(1-p)<5. The adjustment is

For the first two problems, compute the confidence interval in Excel, and statcrunch two ways ("standard" and "Agresti"). Then comment on the differences among the different methods.

1. Eighteen concrete blocks are sampled, and 16 are found to be sufficiently strong. (3 points each part)

a. Demonstrate that the standard formula is not appropriate for this problem (i.e., value of np), and explain why.

b. Using Excel, construct a 95% Confidence interval for the true proportion of blocks that are sufficiently strong. Report on the data from part(a).

c. Using statcrunch (standard), construct a 95% Confidence interval for the true proportion of blocks that are sufficiently strong. Paste the output here.

d. Using statcrunch (Agresti), construct a 95% Confidence interval for the true proportion of blocks that are sufficiently strong. Paste the output here.

e. Comment on the differences among the answers to parts (b)-(d). Do they all make sense?

2. During an economic downturn, 20 companies were sampled, and asked whether they were planning to increase their workforce. Only 3 of the 20 companies were planning to increase their workforce. Comment on any unusual values (3 points each part)

a. Demonstrate that the standard formula is not appropriate for this problem (i.e., value of np), and explain why.

b. Using Excel, construct a 98% Confidence interval for the true proportion of companies that are planning to increase their workforce. Report on the data from part(a).

c. Using statcrunch (standard), construct a 98% Confidence interval for the true proportion of companies that are planning to increase their workforce. Paste the output here.

d. Using statcrunch (Agresti), construct a 98% Confidence interval for the true proportion of companies that are planning to increase their workforce. Paste the output here.

3. A sample using a t-distribution has the following data:

s. mean- 438.29

s. std dev- 15.14

n -17

degree of Freedom- 16

CI % - 0.95

T -2.12

CI low-430.51

CI hi-446.08

What value of n will give a confidence interval of width 10 for this 95% confidence level? (6 points)