Final answer:
The test statistic z = 1.876 is not significant at the 5% level since the p-value of 0.2150 is greater than the significance level of 0.05, leading to the decision not to reject the null hypothesis.
Step-by-step explanation:
You asked if a test statistic of z = 1.876 is significant at the 5% level (α = 0.05) for testing the null hypothesis h0: μ = 0 against the alternative hypothesis h1: μ ≠ 0. To determine the significance of the test, we compare the p-value to the significance level, α (alpha). If the p-value is less than or equal to α, we reject the null hypothesis; if it is greater, we do not reject it.
In this case, the p-value is given as 0.2150. This p-value is greater than the significance level of 0.05. Therefore, our decision is not to reject the null hypothesis because α < p-value. The conclusion is that at the 5 percent significance level, there is insufficient evidence to conclude that the mean (μ) is different from 0.