Question

Think about a population mean that you may be interested in and propose a confidence interval problem for this parameter. Your data values should be approximately normal. For example, you may want to estimate the population mean number of times that adults go out for dinner each week. Your data could be that you spoke with seven people you know and found that they went out 2, 0, 1, 5, 0, 2, and 3 times last week. You then would choose to calculate a 95% (or another level) confidence interval for the population mean. Assume a random sample was chosen which is required to determine a confidence interval.

a) Determine the standard deviation of the given sample.
b) Identify the confidence level for the desired interval.
c) Calculate the margin of error for the proposed confidence interval.
d) Choose the critical value for a 95% confidence interval.

Answer 1

To calculate the confidence interval for the population mean, we need the sample mean, standard deviation, and confidence level. The margin of error is the maximum distance between the sample mean and the true population mean. For a 95% confidence interval, the critical value is 1.96.

Step-by-step explanation:

To calculate the confidence interval for the population mean, we need a sample mean and a standard deviation.

a) To find the standard deviation, we calculate the sample deviation by finding the average of the squared differences between each data value and the sample mean, then taking the square root of that average.

b) The confidence level for the desired interval is given as 95%.

c) The margin of error is calculated by multiplying the standard deviation by the critical value, which is determined based on the desired confidence level. The margin of error represents the maximum distance between the sample mean and the true population mean.

d) For a 95% confidence interval, the critical value is 1.96.