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a random sample of size 20 is selected from a normal population for which the population standard deviation is unknown. assume the null hypothesis indicates a two-tailed test and the researcher decides to use the 0.01 significance level. what values of t will cause the researcher to not reject the null hypothesis?

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∣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.

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