Question

A simple random sample of 101 cities and counties in the United States was selected and the number of positive COVID-19 cases per 1000 citizens was recorded for each. The mean number of positive cases for this sample of 101 counties and cities was 253, with a standard deviation of 11.4. Due to a couple of cities with extremely high numbers of cases the distribution is skewed heavily to the right. If appropriate, use this information to calculate and interpret a 99% confidence interval for the mean number of positive COVID-19 cases per 1000 citizens for all counties and cities in the United States

Answer 1

Sol;

n=101

xbar=sample mean=253

s=11.4

alpha=0.01

alpha/2=0.01/2=0.005

df=n-1=101-1=100

t crit for 100 df and 0.005 level of significance in excel is

=T.INV(0.005,100)

=2.625890521

99% confidence interval for the mean number of positive COVID-19 cases per 1000 citizens for all counties and cities in the United States

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

253-2.625890521*11.4/sqrt(101),253+2.625890521*11.4/sqrt(101)\

250.0213, 255.9787

we are 99% confident that the true mean number of positive COVID-19 cases per 1000 citizens for all counties and cities in the United States lies in between 250.0213 and 255.9787