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

Question

ov 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 176 of 200 test seeds sprout. Perform a significance test at = 0.05 to determine if the seeds have lost viability during a year in storage (i.e., is the proportion of seeds that will sprout less than 92%). 1. Hypotheses Test statistic: P-value: Conclusion:

Explanation / Answer

we know that the test statistic is given as

Z = (phat-p)/sqrt(p*(1-p)/n) , n = 200

we are given that p = 0.92 and phat = 197/200 = 0.88

Putting the values in the equation

z = (0.88-0.92)/sqrt(0.92*(0.08)/200)
= -2.085

now considering alpha = 0.05 , we find the critcal value as -1.644

Hypothesis test is
H0 : The germination rate is 92%
H1: The germination rate is less than 92%

we check the p value from the z table as

Since P ( Z<2.085 )=0.9817, we conclude that:
P ( Z<2.085 )=1P ( Z<2.085 )=10.9817=0.0183

as the p value is less than 0.05 , hence we reject null hypothesis in favor of alternate hypothesis

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