Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 144 people from the city. The average height of your sample is 66 inches, while the standard deviation of the heights in your sample is 3 inches.
The standard error of your estimate of the average height in the city is:___________.

Statisticians use various methods of measuring the uncertainty and reliability of parameter estimates. One of these measures is the standard error of a sample mean, which is computed as the standard deviation of the sample divided by the square root of the sample size.

In this case, since the standard deviation of the sample is 3 inches and the sample size is 144, the standard error of your sample mean is 3144√=312=0.25.

A useful rule of thumb is that the true value of the parameter lies within the range of two standard errors on either side of the parameter estimate, 95 percent of the time. In this case, this means that the true average height of people in the city lies between 66−(2×0.25) and 66+(2×0.25) inches, with 95 percent certainty.

fichoh fichoh · Answer 2 · 2021-10-31T11:45:12+01:00

Using the standard error formula, the standard error of the estimated average height in the city is 0.25 inches.

Given the Parameters :

Sample size, n = 144 people

Standard deviation, σ = 3 inches

Recall the standard error Formula :

[tex] S.E = \frac{σ}{\sqrt(n)} [/tex]

Plugging the values into the formula :

[tex] S.E = \frac{3}{\sqrt(144)} = \frac{3}{12} = 0.25[/tex]

Therefore, the standard error of the average height estimate is 0.25 inches.

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