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
1 answer:
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
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Answer:
see explanation
Step-by-step explanation:
Calculate the slopes between pairs of the 3 points using the slope formula
m =
with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)
m = =
=
= 1
Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)
m = =
= - 1
If lines are perpendicular then the product of their slopes = - 1 , then
1 × - 1 = -1
Thus there is a right angle between the 2 lines
Then triangle is right- angled