Answer:
The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
Step-by-step explanation:
In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.
The hypothesis can be defined as follows:
<em>H</em>₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. <em>p</em> ≤ 0.04.
<em>H</em>ₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. <em>p</em> > 0.04.
The information provided is:
<em>X</em> = 12
<em>n</em> = 200
<em>α</em> = 0.025
The sample proportion of defective chips is:
Compute the test statistic as follows:
The test statistic value is 1.44.
Decision rule:
We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.
Compute the <em>p</em>-value of the test:
The <em>p</em>-value of the test is 0.075.
<em>p</em>-value = 0.075 > <em>α</em> = 0.025
The null hypothesis was failed to be rejected at 2.5% level of significance.
Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.