Final answer:
The margin of error for a 95% confidence interval for the population mean height of adult men is calculated using the Z-score for 95% confidence level, the population standard deviation, and the sample size, resulting in a margin of error of 2.36 cm.
Step-by-step explanation:
The student is asking how to calculate the margin of error for a 95% confidence interval for the population mean height of adult men, given the sample mean, population standard deviation, and sample size. To find the margin of error, we use the Z-score for the desired level of confidence (which is 1.96 for 95%) and the population standard deviation (σ = 7.62 cm). The formula to calculate the margin of error (E) is:
E = Z * (σ / √n)
where Z is the Z-score, σ is the population standard deviation, and n is the sample size.
Plugging in the values we have:
E = 1.96 * (7.62 / √40)
Now, calculate the value under the square root:
E = 1.96 * (7.62 / 6.3246)
Then, perform the division:
E = 1.96 * 1.2042
Lastly, multiply to find the margin of error:
E = 2.36 cm
Therefore, the margin of error for a 95% confidence interval for the population mean height is 2.36 cm.