Question

Confidence Interval Swetha, who joined the Imperial Bank of Hyderabad as an analyst, is trying to estimate the 95 percent two-sided confidence interval for the average monthly profits of tiny units owned by women entrepreneurs. She asked her assistant Rangaswamy to collect the data from 100 tiny units, selected randomly. Based on the sample average given to her by Rangaswamy, she calculated a 95 percent confidence interval using the population standard deviation, σ, which was obtained from the earlier data available in the bank and prepared her report for the managing committee of the bank. After she had completed her report, Rangaswamy told her that he could cover only 64 units and the sample average that he had given her is based on data from 64 units only. When she recalculated the confidence interval (same confidence level) she noticed that the lower limit of the interval had shifted by Rs. 392, as compared to the previous interval. 1. What is the value of σ that Swetha used in the calculation of the confidence interval? 2. What is the width of the confidence interval when Swetha reduced the confidence level to 90 percent? 3. What are the lower and upper limits of a 95% confidence interval (two-sided) based on the above sample, if the sample mean turned out to be 201,200? 4. The sample mean calculated from the data is 201,200. Swetha decided to use the standard deviation, s, obtained from the sample (sample of 64 observations) in the calculation of a 99% confidence interval (two-sided) for μ. What are the upper and lower limits of this confidence interval, if s = 10,500? 5. Swetha wanted a 99 percent confidence interval. She also wanted that width of the interval should not be more than Rs. 2575. What should be minimum sample size that will meet the above requirements? (assume that σ = 10,000 for this purpose)

Answer 1

The confidence interval for mean is

1)The shift of lower limit of the intervals for is

2) The width of the CI is

3) The 95% confidence interval is

4) When the population standard deviation is not known, the confidence interval for mean is

The 99% confidence interval is

5) We need, the width of the CI

The minimum sample size that will meet the above requirements is .