Question

An Austrian study was completed to determine if untrained sea lions and sea lionesses could follow various experimenter-given cues when given a choice of two objects. One experimenter-given cue was to point at one of the objects. One sea lioness, named Zwerg, successfully chose the pointed-at object 37 times out of 48 trials. Does this result show that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time?ââ

Answer 1

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.

What are the hypothesis?

• 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:

$H_1: p > 0.5$

Test statistic

The test statistic 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 test statistic 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 right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, 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