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Sagot :
Answer:
We reject H₀
Step-by-step explanation:
Normal Distribution with n = 22 ( sample size)
n<30 we need to use a t-student distribution
Sample mean μ = 396
Population mean ( required mean ) μ₀ = 405
Sample variance is 441 then sample standard deviation s = √441
s = 21
Hypothesis Test
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ < μ₀
Significance level α = 0,1
The test is a one-tail test to the left
From t-student table we find for t(c)
degree of fredom df = 22 -1 df = 21
and α = 0,1 t(c) = - 1,3232
To compute t(s)
t(s) = ( μ - μ₀ ) / s /√n
t(s) = ( 396 - 405 )*√n / 21
t(s) = - 9 *4,69 /21
t(s) = - 2,01
Comparing
t(s) and t(c) - 2,01 and - 1,3232
|t(s)| > |t(c)| then t(s) is in the rejection region we must reject H₀
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