A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is 5.

a. What is the standard error of the mean (to 2 decimals)?
b. At 95% confidence, what is the margin of error (to 2 decimals)?

A) 0.79

B) 1.55

Part a)

SE of mean = sd/√n = 5/√40

Part b)
ME = 1.96 * 5/√40

I'll let you finish the calculations.

.80

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

Standard Error = population standard deviation / square root of sample size

Given that the population standard deviation is 5 and the sample size is 40, we can compute the standard error:

Standard Error = 5 / √40 = 0.79 (rounded to 2 decimals)

b. To determine the margin of error at a 95% confidence level, we need to account for the critical value associated with the confidence level. Since it is not mentioned whether the distribution is normal or not, we'll assume it is and use the standard normal distribution (z-distribution).

The critical value for a 95% confidence level with a two-tailed test is approximately 1.96.

Margin of Error = critical value * standard error

Margin of Error = 1.96 * 0.79 = 1.55 (rounded to 2 decimals)

So, at a 95% confidence level, the margin of error is 1.55.

To find the standard error of the mean, you will need to use the formula:

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

a. Given that the population standard deviation is 5 and the sample size is 40, you can calculate the standard error of the mean using the formula:
Standard Error of the Mean = 5 / √40

Calculating √40, we find that the square root of 40 is approximately 6.32.

Now, divide 5 by 6.32 to find the standard error of the mean:
Standard Error = 5 / 6.32 ≈ 0.79

So, the standard error of the mean is approximately 0.79 (to 2 decimals).

b. To find the margin of error at 95% confidence, you will need to use the formula:
Margin of Error = Critical Value * Standard Error

The critical value for a 95% confidence level can be found by referring to the z-table or using a calculator. For a standard normal distribution, the critical value for a 95% confidence level is approximately 1.96.

Now, substitute the value of the standard error (0.79) and the critical value (1.96) into the formula:
Margin of Error = 1.96 * 0.79 ≈ 1.55

So, the margin of error at 95% confidence is approximately 1.55 (to 2 decimals).