In: Statistics and Probability
A company produces electric devices operated by a thermostatic control. The standard deviation of the temperature where the controls operate should not exceed 2.0 degrees Fahrenheit. For a random sample of 20 of these controls, the sample standard deviation of operating temperatures was 2.36 degrees Fahrenheit.
i) Stating any necessary assumptions, test, at the 5% level, the null hypothesis that the population standard deviation is 2.0 against the alternative that it is larger.
ii) Create a 90% confidence interval for the population variance.