To calculate Cohen's d, we need the population mean, the sample mean, and the pooled standard deviation.
Given:
Population mean: $\mu = 46$
Sample mean: $\bar{X} = 47$
Sample variance: $s^2 = 16$
To calculate the pooled standard deviation, we can use the formula:
$$s_p = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}}$$
where $n_1$ and $n_2$ are the sample sizes, and $s_1$ and $s_2$ are the sample standard deviations.
Since we only have information for one sample, we can use the sample variance as an estimate for the population variance:
$$s^2 \approx \sigma^2$$
Substituting the given values in the formula, we have:
$$s_p = \sqrt{\frac{(n-1)s^2}{n-1}} = s$$
where $n$ is the sample size.
Therefore, the pooled standard deviation is equal to the sample standard deviation:
$$s_p = s = \sqrt{16} = 4$$
Now we can calculate Cohen's d, which is the difference between the sample mean and the population mean, divided by the pooled standard deviation:
$$d = \frac{\bar{X} - \mu}{s_p} = \frac{47 - 46}{4} = \frac{1}{4} = 0.25$$
Answer: The value of Cohen's d is 0.25.