# Calculation of Confidence Interval and Sample Size

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1) Suppose a fast food restaurant wishes to estimate average sales volume for a new menu item. The restaurant has analyzed the sales of the item at a similar outlet and observed the following results:

X = 500 (mean daily sales)

s = 100 (standard deviation of sample)

n = 50 (sample size)

The restaurant manager wants to know into what range the mean daily sales should fall 95 percent of the time. Perform the calculation.

2) Suppose you are planning to sample cat owners to determine the average number of cans of cat food they purchase monthly. The following standards have been set: a confidence level of 95 percent and an error of less than five units. Past research has indicated that the standard deviation should be 6 units. What is the required sample size?

3) In a survey of 500 people, 60 percent responded with agreement to an attitude question. Calculate a confidence interval at 95 percent to get an interval estimate for a proportion.

4) A researcher expects the population proportion of Cubs fans in Chicago to be 80 percent. The researcher wishes to have an error of less than 5 percent and to be 95 percent confident of an estimate to be made from a mail survey. What sample size is required?

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This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Confidence Intervals and provides students with a clear perspective of the underlying concepts.

###### Education

- MSc, Osmania University
- MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
- BSc, Banaras Hindu University

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