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

Answer:

We reject H₀

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

Step-by-step 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