Answer:
The test statistic for the appropriate test is
.
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:
H₀: There is no difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ = p₂.
Hₐ: There is a difference in proportion of starfish over 8 inches in length in the two ocean areas, i.e. p₁ ≠ p₂.
The two-proportion z-test would be used to perform the test.
A sample of n = 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)[(1)/(n_(n))+(1)/(n_(s))]}}](https://img.qammunity.org/2021/formulas/mathematics/high-school/f709rp5uoln7azfjgjyk80hsfxkloudiqx.png)
Compute the combined proportion P as follows:

Compute the test statistic value as follows:
![z=\frac{\hat p_(n)-\hat p_(s)}{\sqrt{P(1-P)[(1)/(n_(n))+(1)/(n_(s))]}}](https://img.qammunity.org/2021/formulas/mathematics/high-school/f709rp5uoln7azfjgjyk80hsfxkloudiqx.png)
![=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[(1)/(40)+(1)/(40)]}}](https://img.qammunity.org/2021/formulas/mathematics/high-school/i6qp2gkfutt3bz8aqkwfq9rbqkhit6vl43.png)
Thus, the test statistic for the appropriate test is
.