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Answer:
If the scientist’s estimate about the number of fish in the lake is correct, then it is 44% likely to get 20 perch out of 50 with a tag.
Step-by-step explanation:
Let p be the proportion of tagged white perch in the Midwestern lake.
Scientist's claim is that p=
Let's test this hypothesis as:
p=0.30
p≠0.30
P-value of the test statistic will give the likelihood of getting 20 perch out of 50 with a tag if the scientist's estimate () is true.
Test statistic can be calculated using the equation
where
- p(s) is the sample proportion of white perch (
)
- p is the proportion assumed under null hypothesis. (0.30)
- N is the sample size (50)
Then ≈ -0.77
Two tailed p-value of the test statistic is ≈ 0.44
Thus if the scientist’s estimate about the number of fish in the lake is correct, (p=0.30) then it is 44% likely to get 20 perch out of 50 with a tag.