Describe 90% confidence interval for the true proportion.
1. As a help to the establishment of personnel requirements the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director arbitrarily selects 64 different 24-hour periods as well as determines the number of admissions for each. For this sample = 19.8 and s2 = 25. Using the sample standard deviation as an approximate for the population standard deviation what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?
2. A university dean is attentive in determining the proportion of students who receive some sort of financial help. Rather than study the records for all students the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to approximate the true proportion of students who receive financial aid.
3. An economist is attentive in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1000. A random sample of 50 individuals caused in an average income of $15,000. Explain what total sample size would the economist want to use for a 95% confidence interval if the width of the interval must not be more than $100?
a) n = 1537
b) n = 385
c) n = 40
d) n = 20