Question

An article in Cancer Research [“Analyses of Litter-Matched Time-to-Response Data, with Modifications for Recovery of Interlitter Information” (1977, Vol. 37, pp. 3863–3868)] 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 Calculate a 95% confidence interval on the standard deviation of time until a tumor appearance. Check the assumption of normality of the population and comment on the assumptions for the confidence interval

Answer 1

Answer:

2.51 < σ < 3.92

Step-by-step explanation:

We will use Chi-Square distribution to create the interval.  We have the following information:

n = 41

Level of Confidence : 95%,

This corresponds to Chi-Square values of:

24.433 for the left tail and 59.342 for the right tail

We need to calculate the sample Variance.  This is done on attached photo 1 (the shortcut formula for finding variance was used)

We get s = 9.3866.

See the construction of the confidence interval on the second attached photo