Question

Information on a packet of seeds claims that 93% of them will germinate. Of the 200 seeds that I planted, only 175 germinated. (a) Find a 95% CI on the true proportion of seeds that germinate based on this sample. (b) Does this seem to provide evidence that the claim is wrong

Answer 1

We reject H₀

we accept Hₐ seeds in the packet would germinate smaller than 93%

Explanation:

Test of proportions

One tail-test (left side)

93 % = 0.93

p₀ = 0,93

1.- Hypothesis

H₀ ⇒ null hypothesis p₀ = 0.93

Hₐ ⇒ Alternative hypothesis p = 0.875

2.-Confidence interval 95 %

α = 0,05

and

z(c) = - 1.64

3.- Compute z(s)

z(s) = (p - p₀)/√(p₀*q₀)/n z(s) = (0.875-0.93)/√0.93*0.07)200

z(s) = - 0,055/ √0.0003255

z(s) = - 0.055/ 0.018

z(s) = - 3,06

4.-Compere z(c) and z(s)

z(s) < z(c) -3.06 < -1.64

z(s) is in rejection region, we reject H₀