Question

Salaries of 34 college graduates who took a statistics course in college have a mean, x, of $69,700. Assuming a standard deviation, o, of $11,441, construct a 95% confidence interval for estimating the population mean μ. Click here to view a t distribution table Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table (Round to the nearest integer as needed.)

Answer 1

To construct a 95% confidence interval for estimating the population mean μ, calculate the margin of error using the critical value and formula, and then substitute the values into the formula for the confidence interval.

Step-by-step explanation:

To construct a 95% confidence interval for estimating the population mean μ:

1. Calculate the margin of error using the formula: margin of error = (critical value) * (standard deviation / sqrt(sample size)).
2. Find the critical value for a 95% confidence interval using a t-distribution table or calculator.
3. Substitute the values of the sample mean, standard deviation, sample size, and critical value into the formula: confidence interval = sample mean ± margin of error.
4. Round the confidence interval to the nearest integer as needed.

For this specific question, the 95% confidence interval for estimating the population mean μ would be constructed by calculating the margin of error with a critical value of 2.032 (obtained from the t-distribution table for a 95% confidence level with df = n - 1 = 33) and substituting the values of the sample mean, standard deviation, sample size, and critical value into the formula. The confidence interval would be $69,700 ± $3,001, resulting in an interval from $66,699 to $72,701.