Final answer:
The estimated mean height of the population of men represented by this sample with 90% confidence is between 180.21 cm and 181.80 cm, after rounding to the nearest hundredth.
Step-by-step explanation:
To estimate the mean height of the population of men with 90% confidence, we use the sample mean and the standard deviation along with the appropriate z-score for the confidence level.
Given the sample mean (μ) is 181.0 cm, the sample standard deviation (s) is 6.8 cm, and the sample size (n) is 199 men, we apply the formula for the 90% confidence interval for the mean:
μ ± z * (s / √n)
For 90% confidence, the z-score (Ζ) is typically 1.645 (obtained from statistical tables or a z-score calculator).
The margin of error (E) is z * (s / √n), which equals 1.645 * (6.8 / √199). Calculating this gives us E = 0.795 cm
The 90% confidence interval is therefore:
μ ± E = 181.0 cm ± 0.795 cm
This gives a lower bound of 181.0 cm - 0.795 cm = 180.205 cm, and an upper bound of 181.0 cm + 0.795 cm = 181.795 cm.
After rounding to the nearest hundredth, we can estimate the population mean height to be between approximately 180.21 cm and 181.80 cm with 90% confidence.