Respuesta :
Answer:
The test statistic for the appropriate test is [tex]\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}[/tex].
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:
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:
[tex]\hat p_{n}=\frac{6}{40}=0.15[/tex]
Compute the sample proportion of starfish from south that were over 8 inches in length as follows:
[tex]\hat p_{s}=\frac{11}{40}=0.275[/tex]
The test statistic is:
[tex]z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}[/tex]
Compute the combined proportion P as follows:
[tex]P=\frac{X_{n}+X_{s}}{n_{n}+n_{s}}=\frac{6+11}{40+40}=0.2125[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{n}-\hat p_{s}}{\sqrt{P(1-P)[\frac{1}{n_{n}}+\frac{1}{n_{s}}]}}[/tex]
[tex]=\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}[/tex]
Thus, the test statistic for the appropriate test is [tex]\frac{0.15-0.275}{\sqrt{0.2125(1-0.2125)[\frac{1}{40}+\frac{1}{40}]}}[/tex].
