Question

item1 1 points return to questionitem 1 a sample of 14 observations is selected from a normal population where the population standard deviation is 10. the sample mean is 44. a. determine the standard error of the mean. (round the final answer to 3 decimal places.) the standard error of the mean is 2.674 numeric responseedit unavailable. 2.674 correct.. b. determine the 95% confidence interval for the population mean. (round the z-value to 2 decimal places. round the final answers to 3 decimal places.) the 95% confidence interval for the population mean is between 38.759 numeric responseedit unavailable. 38.759 38.759 numeric responseedit unavailable. 38.759 incorrect..

Answer 1

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. The distribution of the sample mean is approximately normal due to the Central Limit Theorem.

Step-by-step explanation:

The standard error of the mean can be calculated using the formula:

Standard Error of the Mean (SEM) = Population Standard Deviation / Square Root of Sample Size

In this scenario, the population standard deviation is 10 and the sample size is 14. So, the SEM = 10 / √14 ≈ 2.674 (rounded to 3 decimal places).

The distribution of the sample mean is approximately normal. This is because of the Central Limit Theorem, which states that for large enough sample sizes, the distribution of sample means will be approximately normal, regardless of the shape of the original population distribution.