A study commissioned by a clothing manufacturer measured the waist size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. to explore how the mean might vary from sample to sample they simualted by drawing many samples of sizes, 2,5,10, and 20 with replacement from the 250 measurements. They summary statistics are shown:
| n |
mean |
st. deviation |
| 2 |
36.314 |
2.855 |
| 5 |
36.314 |
1.805 |
| 10 |
36.341 |
1.276 |
| 20 |
36.339 |
0.895 |
According to the central limit theorem what should the theoretical mean and standard deviation be for each of these sample sizes?
finish the table below
| n |
observed mean |
theoretical mean |
theoretical st.deviation |
| 2 |
36.314 |
36.33 |
|
| 5 |
36.314 |
36.33 |
|
| 10 |
36.341 |
36.33 |
|
| 20 |
36.339 |
36.33 |
|