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Answer:
The test statistic for the appropriate test is .
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:
Compute the combined proportion <em>P</em> as follows:
Compute the test statistic value as follows:
Thus, the test statistic for the appropriate test is .