Hi,

I need some help with a problem. Here is my example that I am studying.

Find a 95% C.I. for the population mean.
Same size 36
N(u, 64)
sample mean 51.8

51.8+-(4/3)(1.96)

Where does the 1.96 come from? 4/3=64/36 so I understand that.

Thanks

Never mind. Figured it out.

Hello! I can help you with that.

The number 1.96 comes from the standard normal distribution table, which is also known as the Z-table. This table gives you the critical values corresponding to different confidence levels.

For a 95% confidence level, we need to find the value that corresponds to an area of 0.025 (since we divide the alpha level by 2 for a two-tailed test). This means we want to find the Z-value that leaves 0.025 of the area in the right tail of the standard normal distribution.

In the Z-table, the area is given in the middle of the table. The values in the table represent the area under the curve to the left of the Z-score. Looking up 0.025 in the table (or finding the closest value), we can see that it corresponds to a Z-score of approximately 1.96.

Therefore, for a 95% confidence interval, we use a Z-value of 1.96. In your case, with a standard deviation of 4/3 and a sample size of 36, you correctly calculated the margin of error as (4/3)(1.96).