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4 years ago

9

If sample data come from a population that is not normally distributed, which

1 answer:

yuradex [85]4 years ago

8 0

Answer:

For a data from population which is not normally distributed, the sample means would be approximately a normal distribution if the sample size (n) is greater than 30

Step-by-step explanation:

For a data from population which is not normally distributed, the sample means would be approximately a normal distribution if the sample size (n) is greater than 30 i.e n ≥ 30 this is because the shape of a sample distribution depends on the sample size. But for normal distribution population, the sample means would be approximately a normal distribution even if the sample size is less than 30;

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c) -2.63.

<h3>What are the hypothesis tested?</h3>

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:

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

<h3>What are the mean and the standard error for the distribution of differences?</h3>

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:

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

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

<h3>What is the test statistic?</h3>

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:

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

$z = \frac{-2 - 0}{0.76}$

z = -2.63.

More can be learned about the z-distribution at brainly.com/question/13873630

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