∣t∣≤2.861, the researcher will not reject the null hypothesis.
To determine the values of t that will cause the researcher to not reject the null hypothesis, we need to look at the critical t-values for a two-tailed test with a 0.01 significance level and degrees of freedom (df) equal to n - 1, where n is the sample size.
For a two-tailed test at a 0.01 significance level, the critical t-values will be in the tails of the t-distribution, and the area in each tail will be 0.005 (0.01 divided by 2). The degrees of freedom (df) for a random sample of size 20 is 19 (20 - 1).
You can find critical t-values using statistical tables or software. However, I can provide you with an approximate value based on common statistical software or calculators.
For a two-tailed test with 19 degrees of freedom and a significance level of 0.01, the critical t-values are approximately ±2.861. Any calculated t-value within this range will lead to the conclusion of not rejecting the null hypothesis.
So, if ∣t∣≤2.861, the researcher will not reject the null hypothesis.