Statistics 3 --Confidence IntervalWatch
The question is
The managing director of a certain firm has commissioned a survey to estimate the mean expenditure of customers on electrical appliances. A random sample of 100 people were questioned and the research team presented the managing director with a 95% confidence interval of (£128.14, £141.86).
The director says that this interval is too wide and wants a confidence interval of total width £10.
a)Using the same value of , find the confidence limits (upper and lower limits) in this case.
b)Find the level of confidence for the interval in part a.
The managing director is still not happy and now wishes to know how large a sample would be required to obtain a 95% confidence interval of total width no more than £10.
Find the smallest size of sample that will satisfy this request.
(sample mean) +/- 1.96(standard deviation)/sqrt(sample size)
With the upper limit found by using the plus and the lower limit found by using the minus, of course
The confidence width is just 2 lots of 1.96(standard deviation)/sqrt(sample size)
You can form simultaneous equations, as you have the sample size and want to know the sample mean and the standard deviation, and you have the upper and lower limits
For part a there seems to have been a typing or copying issue as it says "using the same value of , "?
For part b you use the confidence width formula and just solve for n (rounding to the next integer)