A garden center wants to store leftover packets of vegetable seeds for sale the

Question

A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year's green bean seeds and plants them as a test. Although the packet claims a germination rate of 92% only 171 of 200 test seeds sprout. Is this evidence that the seeds have lost viability during a year in storage? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Explanation / Answer

Given,

Germination rate p= 92% (hypothesized proprtion)

= 0.92

Population tested n = 200

Actual proportion P = 171/200 = 0.855

Null hypothesis :

Estimated mean = actual mean

Alternate hypothesis :

Estimated mean not equal to actual mean

Z = (P-p) / (p(1-p)/n)^0.5

= (0.855-0.92)/(0.92*0.08/200)^0.5

= - 1.766

Z value at 95% value is 1.96

Z critical > Z actual

Hence we dont reject null hypothesis

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