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 be less likely to germinate a year later. The manager randomly selects a packet of last year's green bean seeds and plants a random sample of 200 of the seeds in the packet as a test. Although the packet claims a germination rate of 95%, only 188 of the 200 test seeds sprout. Consider just one experimental unit - that is, one seed. What is the response variable for that one seed? Categorical or quantitative? Verify the three conditions for using the central limit theorem for inference on pi Conduct a significance test to decide if there is sufficient evidence that the seeds have lost viability during a year in storage. Be sure to state your conclusion in plain English in the context of the problem. Look at the statements for Problem 1 and use them as a template for your conclusion here.

Explanation / Answer

Answer to part a)

The response variable is "germination rate" . it has two levels: Either a seed germinates or not . thus it is a ctegorical variable

.

Answer to part b)

The three conditions of centrel limit theorem for inference on

1. The sample size must me equal or larger than 30

2. NP 10

3. N(1-P) 10

.

Answer to part c)

The test statistic is Z = (P^ - P) / sqrt(P*(1-P)/N)

Z = (188/200 - 0.95) / sqrt(0.95 *0.05/200)

Z = (0.94-0.95)/ 0.0154

Z = -0.65

The P value is : 0.2578 [ can be obtained from the Z table]

Since the P value 0.2578 is greater than 0.05 , we conclude that germination rate is not less than 95% . Thus the seeds do no loss viability during a year in storage.

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