Question

As of Friday morning, health officials have confirmed at least 39,140 total cases in New York State. The estimated population of the state was19.45 million residents in 2019.

1- Construct a 99% confidence interval of the percentage of New Yorkers likely infected and interpret your results.

National Institute of Allergy and Infectious Diseases director Anthony Fauci says 1/1000 New Yorkers likely infected.

2- Many others claim that the percentage of infected New Yorkers is higher than what Dr. Fauci says. Please, conduct appropriate test of hypothesis to test that claim using a significance level 0.01.

Answer 1

1. The 99% confidence interval of the percentage of New Yorkers likely infected is between 0.00199 and 0.00204.

We are 99% confident that the true percentage of New Yorkers likely infected is between 0.00199 and 0.00204.

p	0.0020
q	0.9980
n	19450000
z	2.576
sqrt(p*q/n)	1.01614E-05
me = z*sqrt(p*q/n)	2.61758E-05
p - me	0.00199
p + me	0.00204

2. The hypothesis being tested is:

H0: p 0.5

Ha: p < 0.5

The test statistic, z = (p̂ - p)/√p(1-p)/n = (0.0020 - 0.5)/√0.5(1-0.5)/19450000 = -4392

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that the percentage of infected New Yorkers is higher than what Dr. Fauci says.

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