| MATH 924 | | | | | | NAME: |
| HOMEWORK ASSIGNMENT #2, CLASS 4 |
| A. FIND THE CRITICAL VALUE Z* FOR THE INDICATED CONFIDENCE LEVELS, USING 3 DIFFERENT METHODS |
| METHOD 1: | Look up the z value in the posted z-score table (PDF file). Convert z to z*. |
| METHOD 2: | Use the NORM.S.INV function from Excel to determine z from p. Convert z to z*. |
| | That function is the inverse of the NORM.S.DIST (….TRUE) function, which finds the z value for a given p. |
| METHOD 3: | Use the online calculator at http://statpages.info/pdfs.html |
| | The calculator converts z to p and vice versa. |
| | However, unlike the z-score table, the calculator shows p for both tails, |
| | not just the left tail. This is called the 2 tail probability. |
| B. DETERMINE THE MARGIN OF ERROR, assuming the standard error of the mean (SEM) is 8.5. |
| C. DETERMINE THE LOWER AND UPPER LIMIT OF THE CONFIDENCE INTERVAL, assuming the mean is 105. |
| NOTE: Methods 1,2,3 should all return the same z* value, albeit with different numbers of decimals. |
| For task B and C, use the z* from the z score table (Method 1; has the fewest decimals) |
| Confidence Level | Math you need to do before finding z* | | | | Critical value z* | | | Margin | Confidence Intvl. |
| | | | | | METHOD 1 | METHOD 2 | METHOD 3 | of Error |
| (% of area enclosed) | Total area excluded | | Left area excluded | | from z-score | from EXCEL | from | | lower | upper |
| | in % | as p value | in % | as p value | table (PDF file) | norm.s.inv | website above | | limit |
| | | (2 tail) | | (left tail) | (for left tail p) | (for left tail p) | (for 2 tail p!) |
| 99.5 |
| 99 |
| 98 |
| 95 |
| 90 |
| 85 |
| 80 |
| 75 |
| EXTRA CREDIT: |
| Combine the above formulas into just three Excel cells to calculate the margin of error and C.I. lower & upper limits for any given confidence level. |
| INPUT VALUES | | | | | OUTPUT VALUES |
| Confidence Level (%) | Stand. Error | Mean | | | Margin of Error | C.I. lower limit | C.I. upper limit |
| 95 | 8 | 105 |
| Note: I prefilled the INPUT values, but the idea here is that you should be able to type in the values for any situation you may encounter. |
pbiner
CLASS4HWASSIGNMENT2.xlsx
