# Confidence interval

Please see attached file for full problem description.

The director of the hospital wishes to estimate the number of patients who are admitted to the emergency room during a “full” day (24-hour period).
Assume that historical data shows that the number of patient admitted to the hospital in a “full” day can be approximated by a Normally Distributed Random Variable with a standard deviation s = 3. Assume that a random sample 10 days (24-hour period) patient admission records is collected and given in the following table,

Use the formula (`x ± z s ) to calculate a 98% confidence interval that can be used to estimate the mean number of patient admitted to the hospital. Explain the meaning of i) confidence level; ii) confidence interval.
Assume that, in a), the standard deviation s of the number of patient admitted to the hospital in a “full” day is unknown. For the same collected data set, use the Excel Data Analysis software package to find a 98% confidence interval for estimating the mean daily number of patients admitted to the hospital. Are the widths of the Confidence interval obtained in b) and c) same? Can you explain why?
If the director wishes to estimate the expected number of “full” day admissions to a precision with margin of error ±1 admission with 98% confidence level, what should be the minimal sample size?

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