Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

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

At the null hypothesis, it is tested if Zwerg cannot correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_0: p \leq 0.5$

At the alternative hypothesis, it is tested if Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_1: p > 0.5$

<h3>Test statistic</h3>

The <em>test statistic</em> is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5$

The value of the <em>test statistic</em> is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.7708 - 0.5}{\sqrt{\frac{0.5(0.5)}{48}}}$

$z = 3.75$

Considering a <u>right-tailed test</u>, as we are testing if the proportion is greater than a value, with a <u>significance level of 0.05</u>, the critical value for the z-distribution is $z^{\ast} = 1.645$ .

Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

To learn more about the z-distribution, you can take a look at brainly.com/question/16313918

3 0

2 years ago

What is the mean of the data set?

Korvikt [17]

10 for k12 students

ur welcome

4 0

3 years ago

Read 2 more answers

If you have 5 tenths of a dollar, how much money do you have

horrorfan [7]

A tenth is 1/10.
5 tenths is 5/10.

5/10 is a fraction that can be made simpler, by dividing by 5, so that the fraction becomes 1/2.

1/2 is a half, so if you have a half a dollar, you have 50 cents.

Hope I helped. :)

8 0

3 years ago