Question

1. Starting on april 20, New York State conducted a statewide antibody study. They reported that 14.9%of those tested were positive for coronavirus antibodies. They tested a random sample of 7,500 people around the state.

1a. How many people out of the 7500 tested positive?

1b. Find a 95% confidence interval for the proportion of New York State residents who have Coronavirus antibodies. Then write and interpretation of the confidence interval.

1c. Is it possible that 20% of the New York State population has Coronavirus antibodies?

Answer 1

1a) We have n = 7500 and p^ = 0.149

The number of people tested positive for Corona virus antibodies = n * p^ = 1118

1b) The 95% confidence interval for population proportion p is

p^ - E < p < p^ + E

Where E = Z​​​​​​a/2* sqrt[ p^ *(1-p^)/n]

For a = 0.05 , Z​​​​​​0.025 = 1.96

E = 1.96* Sqrt [0.149*0.851/7500]

E = 0.008

0.149 - 0.008 < p < 0.149 + 0.008

0.141 < p < 0.157

We are 95% confident that the proportion of New York State residents who have Coronavirus antibodies is between 0.141 and 0.157

1c)

The proportion p = 0.20 does not lie in the above confidence interval so it is not possible that 20% of the New York State population has Coronavirus antibodies