Question

HPV rates are continuing to increase within communities. The easiest way to prevent against HPV is through vaccination, which is done through a series of vaccinations. A person must receive all vaccinations to be fully protected. A community health worker developed a model to predict HPV vaccination based on address. The health worker predicted that 50% will be completely vaccinated against HPV, 35% partially vaccinated, and 15% receive no vaccination. The observed rates from a sample of the population are detailed below:

	Completely Vaccinated	Partially Vaccinated	No Vaccination
Observed	207	144	99

Using a 0.05 significance and given that the critical value is 5.991, test the claim that the observed frequencies correspond to the expected frequencies.

1. Because critical value is 5.991 and test statistic is 12.85, reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that observed frequencies correspond to the expected frequencies.
2. Because critical value is 5.991 and test statistic is 12.85, reject the null hypothesis and conclude sample data support the claim that observed frequencies correspond to the expected frequencies.
3. Because critical value is 5.991 and test statistic is 17.3, reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that observed frequencies correspond to the expected frequencies.
4. Because critical value is 5.991 and test statistic is 17.3, fail to reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that observed frequencies correspond to the expected frequencies.
5. Because critical value is 5.991 and test statistic is 17.3, reject the null hypothesis and conclude sample data support the claim that observed frequencies correspond to the expected frequencies.

Answer 1

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.500	207	225.00	-1.20	1.440
2	0.350	144	157.50	-1.08	1.157
3	0.150	99	67.50	3.83	14.700
total	1.000	450	450		17.297

from above test statisitc =17.3

hence correct option is C :

Because critical value is 5.991 and test statistic is 17.3, reject the null hypothesis and conclude there is sufficient evidence to warrant rejection of the claim that observed frequencies correspond to the expected frequencies.