Chapter 1 problems
Problem 1.1.
Theoretical explanation:
The three first steps of experiment design can be summarized as:
1. Recognition of the problem and problem statement: During this step, the objective is that of identifying the research question you try to solve through the experiment design. Note that failing to identify the correct research question will imply that you solve a complete different problem, or reach no solution at all.
2. Selection of the response variable: Once you have identified what the problem is, you need to select the variable that you will measure to be able of answering such research question.
3. Choice of factors, levels, and ranges: It is also important to determine where you will analyze your variable and to have an idea of how
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Theoretical explanation: How to search for the p-value?
To calculate the p-value of a hypothesis test where the alternate hypothesis (H1) is stated as µ > µo, you simply need to search for the probability corresponding to the z score in a normal distribution table. The following steps are necessary:
Step 1. Calculate (if unknown) the z score of the hypothesis test.
Step 2. Look up for this value in a normal distribution table. Note that the table is arranged such that the first two digits of z are recorded in the rows of the table, and the third digit of z is recorded on the columns of the table. For instance, if you were searching the p-value corresponding to a z score of 0.43 you would need to search for the row labelled as “0.4” and the column labelled as “0.03”
Step 3. The p-value is the probability that appears in the cell corresponding to the intersection between the selected row and column. In the above example, the p-value would be of 0.3336 as indicated in the figure.
Solution:
Taking this into account, the p-values corresponding to the different z scores would be:
a) P value for z = 2.45: 0.0071
b) P value for z = -1.53: 0.9370
c) P value for z = 2.10: