Question

We are given that n=15, the sample mean Ῡ=2.5, the sample standard deviation s=1.5 and random variable Y distributed Normal with mean µ and variance σ², where both µ and σ² are unknown and we are being concentrated on testing the following set of hypothesis about the mean parameter of the population of interest.

We are to test:

H₀ : µ ≥ 3.0 versus H₁ : µ < 3.0.

Compute the following:

a) P- value of the test

b)    Probability of making Type II error and the power of this test at µ= 2.0

Answer 1

n=15 Ý=2.5 3=1.5 NA a 2 u 73 HA u <3 Hoi t Y-M 2.5-3 1-5 Skis -1.291 plty <-1.291) 10.1088 p-value = (using t-tables) (6) u=2 Power १ (Reject Hol Ho is false) pl Reject to l u=2) P Note : Ho will be rejected if Ý <a - teatas man ie Ý <3-1.7.613 X 1.5 JE < 2.3179 powee < pl ŭ < 2.3179 | 4=2) = P ' y u 2.3179 -M sisu SN- Pl try < 2.3179-2 aus S/AS Pltiuc 0.8207 - 0.7872