Question

The mean yearly income (converted in CAD) for a sample of 48 people in Tol Eressëa is $74987.35. The sample standard deviation is $6098.67. Construct a 95% confidence interval for the mean yearly income of the whole population in Tol Eressëa (round the limits to the unit) Lower limit = Upper limit = [Suggestion: use an online calculator for one of the key ingredients]

Answer 1

To construct a 95% confidence interval for the mean yearly income of the whole population in Tol Eressëa, use the formula CI = X ± (t * (s / sqrt(n))).

Step-by-step explanation:

To construct a 95% confidence interval for the mean yearly income of the whole population in Tol Eressëa, we need to use the formula:

CI = X ± (t * (s / sqrt(n)))

where X is the sample mean, s is the standard deviation, n is the sample size, and t is the critical value from the t-distribution.

In this case, the sample mean is $74,987.35, the standard deviation is $6,098.67, and the sample size is 48.

Using an online calculator, we can find that the critical value for a 95% confidence interval with 47 degrees of freedom is approximately 2.012.

Plugging in the values, we have:

CI = $74,987.35 ± (2.012 * ($6,098.67 / sqrt(48)))

Calculating this, we get a lower limit of $72,717 and an upper limit of $77,257.