Question

A current study by Yang et al. is investigating the rate of false negatives in patients you have COVID-19. In their study, nasal swabs were used on patients known to have COVID-19. Of those 219 swabs, 61 of the tests came back with a false negative. Make a 95% confidence interval for the proportion of all nasal swabs that would return a false negative for people with COVID-19.  Please show all 5 steps, specifically step #3.

Answer 1

Solution :

Given that,

n = 219

x = 61

Point estimate = sample proportion = = x / n = 61/219=0.279

1 -   = 1-0.279 =0.721

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.279*0.721) /219 )

E = 0.0594

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.279- 0.0594< p < 0.279+0.0594

0.2196< p < 0.3384

The 95% confidence interval for the population proportion p is : 0.2196, 0.3384