Final answer:
To determine if the means are statistically the same, conduct a hypothesis test using the Two-Sample Z-Test with known population standard deviations. Compare the calculated Z value to the critical Z value at significance level α=0.05.
Step-by-step explanation:
To determine if the means of the two samples are statistically the same, we can conduct a hypothesis test using the known population standard deviations. We can use the Two-Sample Z-Test to compare the means. We'll set up the null hypothesis H0: μ1 = μ2 (the means are the same) and the alternative hypothesis Ha: μ1 ≠ μ2 (the means are different). We'll use a significance level of α=0.05.
First, we calculate the test statistic Z using the formula: Z = (x1 - x2) / sqrt((σ1^2/n1) + (σ2^2/n2)), where x1 and x2 are the sample means, σ1 and σ2 are the population standard deviations, and n1 and n2 are the sample sizes.
Next, we compare the calculated Z value to the critical Z value for a two-tailed test with α=0.05. If the calculated Z value falls within the critical region, we reject the null hypothesis and conclude that the means are statistically different. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in means.