Question

For each of the following scenarios state whether H0 should be rejected or not. State any assumptions that you make beyond the information that is given.
(a) H0 : µ = 4, H1 : µ 6= 4, n = 15, X = 3.4, S = 1.5, α = .05.
(b) H0 : µ = 21, H1 : µ < 21, n = 75, X = 20.12, S = 2.1, α = .10.
(c) H0 : µ = 10, H1 : µ 6= 10, n = 36, p-value = 0.061.

Answer 1

Answer:

a)$H_0 :\mu = 4\\ H_1 : \mu \neq 4$ , n = 15 , X=3.4 , S=1.5 , α = .05

Formula : $t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{3.4-4}{\frac{1.5}{\sqrt{15}}}$

$t =-1.549$

p- value = 0.607(using calculator)

α = .05

p- value > α

So, we failed to reject null hypothesis

b)$H_0 :\mu = 21\\ H_1 : \mu < 21$ , n =75 , X=20.12 , S=2.1 , α = .10

Formula : $t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{20.12-21}{\frac{2.1}{\sqrt{75}}}$

$t =-3.6290$

p- value = 0.000412(using calculator)

α = .1

p- value< α

So, we reject null hypothesis

(c) $H_0 :\mu = 10\\ H_1 : \mu \neq 10$, n = 36, p-value = 0.061.

Assume α = .05

p-value = 0.061.

p- value > α

So, we failed to reject null hypothesis