Question

1. Determine the critical value of Z for a left tailed test regarding a population mean at the alpha ?= .05 level of significance.

2. Determine the critical value of t for a? two-tailed test of a population mean at the alpha ?= .05 level of significance based on a sample size of n? = 14? (13 d.f.).

3. Determine if the following statement is true or false.

When testing a hypothesis using the? P-value Approach, if the? P-value is? large, reject the null hypothesis.

Answer 1

1. The critical value of Z for a left tailed test regarding a population mean at the alpha = 0.05 level of significance is given as the probability P(Z < z) = 0.05. From the normal distribution table, P(Z < -1.6449) = 0.05.

The critical value of Z for a left tailed test regarding a population mean at the alpha = 0.05 level of significance is -1.6449.

2.

The critical value of t for a two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14 (13 d.f) is given as the probability (t1 < t₁₃ < t2) = 0.05.

From the t-distribution table,

P(-2.16 < t₁₃ < 2.16) = 0.05

So the critical value for a two-tailed test of a population mean at the alpha = 0.05 level of signfiicance based on a sample size of n = 14 (13 d.f.) is 2.16.

3.

The statement "When testing a hypothesis using the P-value Approach, if the P-value is large, reject the null hypothesis" is false as the correct statement is "When testing a hypothesis using the P-value Approach, if the P-value is large, we cannot reject the null hypothesis".