1. Suppose we wish to find the required sample size to find a90% confidence interval for the population proportion with thedesired margin of error. If there is no roughestimate   of the population proportion, what valueshould be assumed for  ?
2. An analyst takes a random sample of 25 firms in thetelecommunications industry and constructs a confidence intervalfor the mean return for the prior year. Holding all else constant,if he increased the sample size to 30 firms, how are the standarderror of the mean and the width of the confidence intervalaffected?
| Standard error of the mean | Width of confidence interval |
| A | Increases | Becomes wider |
| B | Increases | Becomes narrower |
| C | Decreases | Becomes wider |
| D | Decreases | Becomes narrower |
| | 1.96(10.24/6) |
| | 1.96(3.20/6) |
| | 1.645(3.20/6) |
| | 1.645(10.24/6) |
3. For a given confidence level and population standarddeviation, which of the following is true in the intervalestimation of the population mean?
| | If the sample size is bigger, the interval is narrower. |
| | If the population size is smaller, the interval is narrower. |
| | If the population size is bigger, the interval is narrower. |
| | If the sample size is smaller, the interval is narrower. |
