Question

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Answer 1

Using the z-distribution, the p-value would be of:

b) 0.0086.

What are the hypothesis tested?

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

$H_0: \mu_D - \mu_C = 0$

At the alternative hypothesis, we test if they are different, hence:

$H_1: \mu_D - \mu_C \neq 0$

What are the mean and the standard error for the distribution of differences?

For each sample, they are given as follows:

• $\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086$.

• $\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556$.

For the distribution of differences, it is given by:

• $\overline{x} = \mu_D - \mu_C = 12 - 14 = -2$.

• $s = \sqrt{s_D^2 + s_C^2} = \sqrt{0.6086^2 + 0.4556^2} = 0.76$

What is the test statistic?

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$z = \frac{\overline{x} - \mu}{s}$

z = -2/0.76

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

More can be learned about the z-distribution at brainly.com/question/16313918

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