Answer:
The test statistic for the appropriate test is ![\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}](https://tex.z-dn.net/?f=%5Cfrac%7B0.15-0.275%7D%7B%5Csqrt%7B0.2125%281-0.2125%29%5B%5Cfrac%7B1%7D%7B40%7D%2B%5Cfrac%7B1%7D%7B40%7D%5D%7D%7D)
.
Step-by-step explanation:
The experiment conducted here is to determine whether there is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. north and south.
The hypothesis to test this can be defined as follows:
<em>H₀</em>: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ = <em>p</em>₂.
<em>Hₐ</em>: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. <em>p</em>₁ ≠ <em>p</em>₂.
The two-proportion <em>z</em>-test would be used to perform the test.
A sample of <em>n</em> = 40 starfishes are selected from both the ocean areas.
It provided that of the 40 starfish from the north, 6 were found to be over 8 inches in length and of the 40 starfish from the south, 11 were found to be over 8 inches in length.
Compute the sample proportion of starfish from north that were over 8 inches in length as follows:
Compute the sample proportion of starfish from south that were over 8 inches in length as follows:
The test statistic is:
![z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B%5Chat%20p_%7Bn%7D-%5Chat%20p_%7Bs%7D%7D%7B%5Csqrt%7BP%281-P%29%5B%5Cfrac%7B1%7D%7Bn_%7Bn%7D%7D%2B%5Cfrac%7B1%7D%7Bn_%7Bs%7D%7D%5D%7D%7D)
Compute the combined proportion <em>P</em> as follows:
Compute the test statistic value as follows:
![=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0.15-0.275%7D%7B%5Csqrt%7B0.2125%281-0.2125%29%5B%5Cfrac%7B1%7D%7B40%7D%2B%5Cfrac%7B1%7D%7B40%7D%5D%7D%7D)
Thus, the test statistic for the appropriate test is .
