We are managing a large soy bean farm. To estimate our revenues for the coming year,
we need to estimate our crop yield. Soy bean yields are measured by pods/plant. We are
planning for a yield of 40 pods/plant.
a. We take a random sample of 64 soy bean plants and get a sample mean yield of 38.6
pods/plant with a sample standard deviation of 4.8 pods/plant. Assuming that our
population pods/plant is 40, what is the probability of obtaining the sample we got or one
that varies more in the same direction from the assumed mean? (Use Minitab.)
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To calculate the probability of obtaining the sample you got or one that varies more in the same direction from the assumed mean, you can use a one-sample t-test and compare the sample mean to the assumed population mean.
Here's how you can use Minitab to calculate the probability:
1. Open Minitab and go to "Stat" → "Basic Statistics" → "1-Sample t".
2. In the "One-sample t" dialog box, enter your sample data in the "Sample data" field. For example, enter "38.6" in the first row and so on until all 64 values are entered.
3. In the "Test mean" field, enter the assumed population mean, which is 40 in this case.
4. In the "Options" area, make sure the "Perform hypotheses test" box is checked.
5. Click "OK" to run the analysis.
Minitab will perform a one-sample t-test and provide you with the p-value, which represents the probability of obtaining the sample mean value or one that varies more in the same direction from the assumed mean.
Note: The specific p-value calculation depends on the software and settings you use, so refer to the output generated by Minitab for the exact value.
The resulting p-value will indicate whether the observed sample mean of 38.6 pods/plant is significantly different from the assumed population mean of 40 pods/plant. The lower the p-value, the less likely it is to obtain a sample mean as extreme as the one observed, assuming the population mean is 40 pods/plant.