An article in Cancer Research [Analyses of Litter-Matched Time-to-Response Data, with Modifications for Recovery of Interlitter Information (1977, Vol. 37, pp. 38633868)] tested the tumorigenesis of a drug. Rats were randomly selected from litters and given the drug. The times of tumor appearance were recorded as follows:

101, 104, 104, 77, 89, 88, 104, 96, 82, 70, 89, 91, 39, 103, 93, 85, 104, 104, 81, 67, 104, 104, 104, 87, 104, 89, 78, 104, 86, 76, 103, 102, 80, 45, 94, 104, 104, 76, 80, 72, 73

a.)Calculate a 95% confidence interval on the standard deviation of time until a tumor appearance.

(Data is assumed to be normally distributed)

b.)Build a hypothesis test (state null and alternative hypotheses) for the standard deviation of tumor appearance time such that at a significance level of = 0.05 we fail to reject the null hypothesis.

(Just state the related H₀ and H₁)