Final answer:
Since the 95% confidence interval for an independent means t-test does not include the value of 0 and lies between 1.547 and 4.587, we reject the null hypothesis, indicating there is a statistically significant difference. Given this situation, the statistical decision aligns with option (1) reject the null hypothesis.
Step-by-step explanation:
When considering an independent means t-test with a 95% confidence interval that lies between 1.547 and 4.587, it is important to examine whether 0 is within this confidence interval. Since 0 is not included within the interval of 1.547 to 4.587, this suggests that the difference between group means is significantly different from 0. Thus, we conclude that there is a statistically significant difference and, therefore, reject the null hypothesis. In the context of hypothesis testing, the null hypothesis (typically denoted as H0) posits that there is no effect or no difference. When the confidence interval does not contain the value of no effect (in this case, 0 for the mean difference), we have evidence against the null hypothesis. Given this situation, the statistical decision aligns with option (1) reject the null hypothesis.