Answer :
The 95% Confidence Interval suggests that we are 95% confident that the true mean height of all men lies within the range of 169.792 cm to 182.208 cm.
To calculate the 95% Confidence Interval for the mean height of the randomly chosen men, we can use the following formula.
Confidence Interval = mean ± (Z * (standard deviation / √n))
To find the Z-score for a 95% confidence level, we need to divide the desired confidence level by 2 (since we are looking for a two-tailed test) and find the Z-score corresponding to the resulting area under the standard normal distribution curve. For a 95% confidence level, the resulting area is 0.975.
Using a Z-table or a calculator, we find that the Z-score corresponding to an area of 0.975 is approximately 1.96.
Now we can plug in the values into the formula:
Confidence Interval = 176 ± (1.96 * (20 / √40))
Calculating this, we get:
Confidence Interval = 176 ± (1.96 * (20 / 6.324))
Simplifying further:
Confidence Interval = 176 ± (1.96 * 3.167)
Confidence Interval = 176 ± 6.208
Therefore, the 95% Confidence Interval for the mean height of the randomly chosen men is (169.792 cm, 182.208 cm).
In conclusion, the 95% Confidence Interval suggests that we are 95% confident that the true mean height of all men lies within the range of 169.792 cm to 182.208 cm.
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