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bogdanovich [222]
2 years ago
15

Please Help! Multiple Choice!

Mathematics
1 answer:
Katyanochek1 [597]2 years ago
4 0

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

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

At the null hypothesis we test if the means are equal, hence:

H_0: \mu_D - \mu_C = 0

At the alternative hypothesis, it is tested 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

Hence, for the distribution of differences, they are given by:

  • \overline{x} = 12 - 14 = -2.
  • s = \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.

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

Hence option B is correct.

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

#SPJ1

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