At a Bloomburg City Council meeting, a plan to fund more swim
safety programs was presented. The reasoning behind the request was
that less than 40% of children under the age of 5 could pass a swim
test. If this is true, the council will agree to fund more programs
for these kids. The council decides to take a 200-person volunteer
sample of children under 5 years in Bloomburg City and conduct a
significance test for H0: p = 0.40 and Ha: p < 0.40, where p is
the proportion of these children that can pass a swim test. They
will perform a significance test at a significance level of α =
0.05 for the hypotheses.
Part A: Describe a Type II error that could
occur. What impact could this error have on the
situation?
Part B: Out of the 200 children under 5 that
volunteered to take a swimming test, 87 passed, resulting in a
p-value of 0.8438. What can you conclude from this p-value given
the data of the 200 children is sufficient to perform a
significance test for the hypotheses?
Part C: What possible defect in the study
can you find in Part B? Explain.