Question

As the national government has increased its voiced approval for the HPV vaccine known as Gardasil, many organizations have begun gathering data to address the rise in prevalence of young girls receiving the vaccine. Last year, the National Center for Health Statistics estimated that the National vaccine prevalence is up to 15% in the same age demographic. In order to test this assumption, a researcher conducted a study and found that out of 3,579 women in the demographic surveyed, 879 reported receiving one or more of the three shots included in the package for the vaccine.

A) Is the sample size large enough to justify the use of the Z formula?

B) Test if the proportion of the prevalence of the vaccine has changed. Use = 0.05. Hint: One sample proportion.

C) Calculate the 95% two-sided confidence interval for p and make a conclusion about H₀.

D) Compare your results and conclusions in a and b above. What would you conclude?

Carry probabilities to at least four decimal places for intermediate steps.

For extremely small probabilities, it is important to have one or two significant non-zero digits, for example, 0.000001 or 0.000034.

Round off your final answer to two decimal places.

Answer 1

a)

here n=3579 and p=0.15 ; cause np >=10 and n(1-p) >=10 ; therefore sample size is large enough to justify the use of the Z formula

b)

as test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that  proportion of the prevalence of the vaccine has changed.

c)

as confidennce interval contains value above 0.15 ; therefore we can reject null hypothesis

we have sufficient evidence to conclude that  proportion of the prevalence of the vaccine has changed.

d)

we can see that conclusion from part a and b are same. we can conclude that hypothesis test and confidence interval both approach lead to same result