A recent report states that less than 40% of the children
younger than 5 years in Bloomburg City were able to pass a swimming
test. Consequently, the city's aquatics department is trying to
convince the city council to fund more swimming programs. The
council will fund more programs only if the aquatics department can
provide convincing evidence that the report is true.
Members of the aquatics department plan to collect data from a
sample of 200 children younger than 5 years who live in Bloomburg
City. A test of significance will be conducted at a significance
level of α = 0.05 for the hypotheses H0: p = 0.40 and
Ha: p < 0.40, where p is the proportion of children
who live in the city and are able to pass the swimming test.
Part A: Describe a Type II error in the
context of the study and the consequence of making this type of
error. (3 points)
Part B: Members of the aquatics department
recruit 200 residents younger than 5 years who volunteer to take
the swimming test. The test is passed by 87 of the 200 volunteers,
resulting in a p-value of 0.8438 for the given hypotheses. If it is
reasonable to conduct a test of significance for the given
hypotheses using the data collected from the 200 volunteers, what
does the p-value of 0.8438 lead you to conclude?
Part C: Describe the primary flaw in the
study described in part B and explain why it is a concern.