Sophia and Scott each open a bank account with an initial deposit of $50 each. Scott planned to save 30% of his earnings from hi
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Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.
To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.
A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:
Similarly, but exchanging the role of x and y, we compute the length of BC:
So, the area of the rectangle is
The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:
So, the area of the portion located in the third quadrant is
This means that the ratio between the two area is
If we want this ratio to be a percentage, just make sure that the denominator is 100:
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that
Value of the test statistic:
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.