What term defines the process of analyzing actions

Ответ:

faithyholcomb

10.04.2021

We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.

Null and alternative hypothesis:

Claim the the proportion is of 60%, thus, the null hypothesis is:

H_0: p = 0.6

Test if the proportion is greater than 60%, thus, the alternative hypothesis is:

H_1: p 0.6

And the answer to the first question is given by option c.

Classification:

We are testing if the proportion is greater than a value, so it is a right-tailed test.

Test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.6 is tested at the null hypothesis:

This means that $\mu = 0.6, \sigma = \sqrt{0.4*0.6}$

Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.

This means that n = 100, X = 0.69

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}$

z = 1.837

The test statistic is z = 1.837.

p-value:

The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.

Looking at the z-table, z = 1.837 has a p-value of 0.9669.

1 - 0.9669 = 0.0331

The p-value is 0.0331.

Decision:

The p-value of the test is 0.0331 > 0.01, and thus:

a. Fail to reject the null hypothesis

For another example of a problem of a test of hypothesis, you can take a look at:

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