Question

The mean replacement time for a random sample of 20 washing machines is 10.9 years andthe standard deviation is 2.7 years.a) Which distribution is used to estimate standard deviation?b) Find the critical right value:c) Find the critical left value:d) How many degrees of freedom are in this sample?e) Construct a 99% confidence interval for the standard deviation, Η, of the replacementtimes of all washing machines of this type.f) State your results in non-technicaal language.

Answer 1

a)

We use chi-distribution for estimating confidence interval for Variance and Standard deviation

For a degree of freedom, df = n-1

b)

The critical right value is

c)

The critical left value is

d)

degree of freedom = n-1 = 19

e)

f)

We are 99% confident that true standard deviation of the mean replacement time lies between the range of 1.8947 and 4.4987