Question

The data below gives the survival times of 20 mice exposed to 240 rads of gamma radiation.

152 152 115 109 137 88 94 77 160 165 125 40 128 123 136 101 62 153 83 69

1. Carry out a t-test for whether the mean exceeds 100. Use a t-test with a rejection region and α = 0.05 . You may find the following summaries of the data helpful: x = 113.45, s = 35.79, n = 20

2. Considering the hypothesis test in question 1 above,

a. Calculate the p-value. It can be in a range.

b. Calculate the p-value again, if the alternative hypothesis is instead Ha: : μ =/ 100. As above, your answer can be a range of values.

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 100
Alternative Hypothesis, Ha: μ > 100

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (113.45 - 100)/(35.79/sqrt(20))
t = 1.681

P-value Approach
P-value = 0.0546

0.05 < p-value < 0.1

b)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 100
Alternative Hypothesis, Ha: μ ≠ 100

P-value Approach
P-value = 0.1091

0.1 < p-value < 0.2