Excel for Scientists & Engineers

Estimating with Confidence

Often times, we need to estimate the characteristics of a population on the basis of information about a sample. For instance, we use the sample's mean to estimate the population's mean.

The amount of confidence we can put in an estimate varies. To deal with this problem,

  • we set a confidence level (usually 95%) and

  • we determine a confidence limit (around the mean).

Look at the example shown in Table - 11. Based on a sample's mean of 44 (and a standard error of 6), we have 95% confidence that the population's mean is between 32 and 56. Consequently, we take a 5% risk ( ?) of being wrong!

Table 11: Example of Z-values and probabilities for specific means, given a mean of means of 44 and a standard error of 6

-3

-2

-1

0

1

2

3

Z-value

0%

2%

16%

50%

84%

98%

100%

probability

26

32

38

44

50

56

62

mean

stdev

44

6

-DIST functions find the probabilities (for a certain distance)

-INV functions find the distance (for a certain probability)

If we were to plot "cumulative" means for one up to 20 samples of 10...

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