For each of these problems, conduct a significance test. Remember there are four
ID: 3217089 • Letter: F
Question
For each of these problems, conduct a significance test. Remember there are four steps after confirming the conditions are met for inference:
1) state the hypotheses
2) calculate test statistic
3) find P-value. Remember that we are using = 0.05 as our guideline for statistical significance. If P-value 0.05, reject Ho. If P-value > 0.05, do not reject Ho.
4) state the conclusion in plain English in the context of the problem, not just “reject Ho” or “do not reject Ho.” Look at the statements for Problem 1 and use them as a template for your conclusions. If you decide to reject Ho give the P-value.
Problem 3) 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.
a) Consider just one experimental unit – that is, one seed. What is the response variable for that one seed? Categorical or quantitative?
b) Verify the three conditions for using the central limit theorem for inference on
c) 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
a) categorical as a seed either germinates or not. No numerical characteristics involved
b) Randomization: This condition is assumed as the problem states that a random sample was selected
10% Rule: seeds in a packet come from a large population and therefore is safe to assume 200 is less than 10% of the population
np0=200*.0.95=190, nq0= 200*.0.05=10; As np0 and nq0 are greater than or equal to 10, we can approximate the sampling distribution using normal approximation
c) p0 = 0.95; p = 188/200 = 0.94, n = 200
H0 : p=p0, Ha : p<p0
Left-tailed, directional hypothesis test (since the test is asking for significance of lost viability)
The test statistic formula is:
z = (0.94 - 0.95)/sqrt((0.95*0.05)/200) = --0.64889
p value = 0.2582
We do not have evidence to show that the viability of seeds in the leftover packets is less than 95 percent.
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