Question

A sample of 40 adult men has an average height of 173 cm. Assume the population standard deviation is σ = 7.62 cm. Using Desmos or a scientific calculator, find the margin of error for a 95% confidence interval for the population mean height.

Answer 1

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.