Question

2. Find 95% confidence interval for estimating population standard deviation σ of car batteries given that a random sample of 25 batteries has a standard deviation s -1.5 years.

Answer 1

The (1 - ) confidence interval for standard deviation is,

where n is the sample size, s is the sample standard deviation and $chi^2_{i}$ is the lower i^th point of the $chi^2$ distribution with df 24 [Which can be obtained by MS Excel using the code CHIINV(i.24)].

s = 1.5. n = 25, 1 - = 0.95 => = 0.05, = 12.4011 and = 39.3641.

So, the 95% confidence interval become

=> 1.1712 < < 2.0867