Question

A sample has 236 cases (n=236) and a sample mean of 34.7(x). The population standard deviation (o) is 6.93. (Keep two decimal places in all answers) Answer the following questions in the space below:

A. Calculate the standard error for the sampling distribution of the mean
B. Calculate a 95% confidence interval to estimate the population mean.
C. Interpret your 95% confidence interval

Answer 1

A. The standard error is approximately 0.45. B. The 95% confidence interval is approximately 33.82 to 35.58. C. The true population mean is likely to fall within the confidence interval.

Step-by-step explanation:

A. To calculate the standard error for the sampling distribution of the mean, we use the formula:

Standard Error (SE) = Standard Deviation (σ) / Square Root of Sample Size (n)

SE = 6.93 / √236

SE ≈ 0.45

B. To calculate a 95% confidence interval to estimate the population mean, we use the formula:

Confidence Interval = Sample Mean ± (Critical Value x Standard Error)

Using a 95% confidence level, the critical value is approximately 1.96 (from the z-table).

Confidence Interval = 34.7 ± (1.96 x 0.45)

Confidence Interval ≈ 33.82 to 35.58

C. The interpretation of the 95% confidence interval is that we can be 95% confident that the true population mean falls within the range of 33.82 to 35.58 based on the given sample.