Covid-19 can be devastating. Researchers at JJ Health Services took a random sample of n=3947 hospitalized Covid-19 patients out of a very large population of hospitalized Covid-19 patients. Of these,...

Covid-19 can be devastating. Researchers at JJ Health Services took a random sample of n=3947 hospitalized Covid-19 patients out of a very large population of hospitalized Covid-19 patients. Of these, x = 2903 patients showed a symptom of loss of smell (LOS). Let p be the (unknown) true proportion of Covid-19 patients who show a symptom of LOS. We want to estimate p. X is the random variable representing the number of sampled Covid-19 patients with LOS?

e) Construct a 94% classical confidence interval for p?

f) How long is the 94% classical confidence interval for p?

g) If we are creating a 94% classical confidence interval for p based upon the sample size of 3947, then what is the longest possible length of this interval?