Question

Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using α = 0. 2. One student used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null. Which of these might have been their calculated value of t?

Answer 1

Based on the calculations, the most likely value of t is equal to 2.2.

Given the following data:

• $\alpha =0.2$

What is a null hypothesis?

A null hypothesis ($H_0$) can be defined the opposite of an alternate hypothesis ($H_a$) and it asserts that two (2) possibilities are the same.

For the one-tail test, we would reject the null hypothesis ($H_0$) when the p-value is lesser than the value of $\alpha$;

$H_o: P(Z > |\delta|) < 0.02$

For the two-tail test, we would fail to reject the null hypothesis ($H_0$) when the p-value is greater than the value of $\alpha$;

$H_o: 2P(Z > |z|) > 0.02\\\\H_o: P(Z > |z|) > 0.01$

Next, we would determine the positive value of z-score that satisfies this expression;

$0.01 < P(Z < z) < 0.02$

From the z-table, we have:

$P(Z > 2.326)\;and\; P(Z > 2.054)\\\\2.054 < z < 2.326$

Therefore, t = 2.2.

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