Final answer:
To calculate a 95% confidence interval for the population mean age of Australian males in couples who separated, use the sample mean, the SEM, and the appropriate t-value based on the degrees of freedom. For a sample size of 144, the df is 143. The CI is the sample mean ± (t-value) * SEM.
Step-by-step explanation:
To find a 95% confidence interval for the population mean age of Australian males in couples who separated, we will follow several steps using the sample mean, sample error (SEM), and the sample size provided.
Firstly, we must identify the degrees of freedom (df), which is calculated as the sample size minus one. Therefore, for a sample size of 144, the df is 144 - 1 = 143.
Secondly, we need the appropriate t value for a two-tailed 95% confidence interval. Using a t-distribution table or calculator, we find the t-value that corresponds to the 95% confidence level with the df of 143.
To calculate the confidence interval (CI), the following formula is used:
CI = sample mean ± (t-value) * SEM
To find the 95% CI specifically: CI = 35.65 ± (t-value) * 0.65
Since the student question does not provide the specific t-value, one would typically use technology or a t-distribution table to find this value based on the degrees of freedom.
For the 99% confidence interval, a different t-value (greater in absolute value than the 95% CI t-value) corresponding to the 99% confidence level and 143 df would be used with the same formula as above.
If the sample size had been 30, the degrees of freedom would also be different, affecting the t-value used in the calculation. You would find this new t-value based on the new degrees of freedom (df = 29) and use the same CI formula for the 95% confidence interval, which will likely yield a wider interval due to the smaller sample size.