Final answer:
The statement regarding the Z Statistic with a value between ±1.96 implying a P-Value greater than 0.05 is false, as a Z Statistic in this range corresponds to a two-sided P-Value of exactly 0.05, which is the threshold for the 95% confidence level.
Step-by-step explanation:
The statement 'The Z Statistic Has A Value Between ±1.96. This Implies That The Two-Sided P-Value Is Greater Than 0.05' is false. A z-score of ±1.96 corresponds to a 95% confidence interval, meaning that the area under the normal curve between these two values encompasses 95% of the data. Therefore, the two-sided p-value associated with z-scores of ±1.96 is exactly 0.05, not greater than 0.05. A p-value greater than 0.05 would correspond to z-scores with absolute values less than 1.96. Conversely, if the calculated test statistic were within this range, it would suggest there is insufficient evidence to reject the null hypothesis at a significance level of 0.05.
When performing a two-tailed hypothesis test and your test statistic (z-score) lies between -1.96 and +1.96, the p-value of the test will be greater than 0.05, which typically means the null hypothesis cannot be rejected at the 5% significance level. However, in this context, saying that a z-statistic 'has a value between ±1.96 implies that the two-sided P-Value is greater than 0.05' is not correct because this range corresponds exactly to a p-value of 0.05 for a two-tailed test.