Chapters 18-19 Summative Assessment

Question

1. A national newspaper reported that 10% of Americans have received the vaccine for Covid-19 (as of February 10, 2021). A local community is concerned that their citizens are not being vaccinated at the same rate as the rest of the nation. In a random sample of 150 residents of this community, 8% have received the vaccine. Is there significant evidence that this community’s rate of vaccination is lower than the nation’s? 

1. Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)

1. Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose that kind of test in this situation.

1. Explain what your P-value means in this context.

Answer 1

Ho: p = 0.1

Ha: p < 0.1

phat (sample proportion) = 0.08, n = 150

sample is random, n*phat = 150*0.08 = 12 and n(1-phat) = 150*0.92 = 138 both > 10

sample size less than 10% of the population

test statistic z = (phat - p)/sqrt(p*(1-p)/n) = (0.08 - 0.1)/sqrt(0.1*0.9/150) = -0.82

test is left tailed as looking to test if vaccination rate is LOWER than the national rate

p-value is P(z < -0.82) = 0.2061.

p-value =0.2061 is the probability of getting a proportion as low as 0.08 when the population proportion is 0.1. It is also the lowest level of significance for which the null hypothesis will be rejected. Since the p-value is relatively large, one would fail to reject the null hypothesis and conclude there is insufficient evidence to suggest the community's vaccination rate is lower than the national average.