Question

1. If California has 400769 confirmed cases of COVID-19 and 7,769 deaths related to the disease find as 95% confidence interval for California’s death rate for COVID-19.

Answer 1

We need to find 95% confidence interval for California’s death rate for COVID-19.

Given

n = 400769       [ California has 400769 confirmed cases of COVID-19   ]

x = 7769          [ 7,769 deaths related to the disease or here number of success ]

Thus ,

= x / n                [ Estimate of required proportion from given sample i.e proportion of death rate ]

= 7769 / 400769

= 0.01938523

95% confidence interval for proportion is given by

CI = { - *    ,    + * }

Here , for 95% confidence z-critical value is 1.96

Calculation :-

= 0.01938523     ;   = 1.96

and , = = 0.0002177899

CI = { - *    ,    + * }

CI = { 0.01938523   - 1.96 * 0.0002177899   ,    0.01938523   + 1.96 * 0.0002177899 }

CI = { 0.01895836   ,    0.0198121 }

So , required confidence interval is { 0.018958 , 0.019812 }

Thus , 95% confidence interval for California’s death rate for COVID-19 is { 0.018958 , 0.019812 }

or { 1.8958 % ,   1.9812 % }