20 POINTS Part E How many of the 320 million Americans would you predict wear glasses?
1 answer:
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Using the z-distribution, as we are working with a proportion, it is found that there is enough evidence to conclude that the proportion is different of 50%.
<h3>What are the hypothesis tested?</h3>At the null hypothesis, it is tested if the proportion is of 0.5, that is:
At the alternative hypothesis, it is tested if the proportion is different of 0.5, that is:
.
The test statistic is given by:
In which:
is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are:
Then, the value of the test statistic is as follows:
Considering a <em>two-tailed test</em>, as we are testing if the proportion is different of a value, with a <em>significance level of 0.05</em>, the critical value is of .
Since the absolute value of the test statistic is greater than the critical value for the two-tailed test, it is found that there is enough evidence to conclude that the proportion of participants that had improved androstenone-detection accuracy is different of 50%.
More can be learned about the z-distribution at brainly.com/question/26454209
Given matrices are from here
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Problem 3
a)
B - C = DNE
We cannot subtract matrices of different sizes. Matrix B is 2x2 while C is 3x2. Both matrices must have the same number of rows, and they must also have the same number of columns. The matrices don't have to be square.
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b)
You add the corresponding elements. For instance, in the top left corner we have -1+(-4) = -5. The other entries are treated in a similar manner.
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c)
You get this from multiplying each entry in matrix E by -2. Eg: top left corner has -2*(-3) = 6
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d)
Matrix C has 3 rows and D has 3 columns. The final answer will be size 3x3
To generate each value in the answer matrix, you'll highlight rows of C to pair with columns of D. Then you'll multiply out the corresponding values, after which you add those products. This is done for every entry in the answer shown above.
For example, the first row of C is highlighted and the second column of D is highlighted. Those values pair up and multiply getting -1*(-1) + 2*3 = 1+6 = 7, which goes in the first row and second column of the answer matrix. The other entries are handled in a similar fashion.
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e)
The 2x2 matrix determinant formula is
In this case, a = -4, b = 6, c = 5, d = 4.
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f)
Swap the top left and bottom right corners of matrix B. Change the sign of the other two corner values. Then multiply each entry by 1/d where d is the determinant found back in part (e) above. Be sure to reduce any fraction as much as possible.
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Problem 4
Answers: x = 2 and y = -10
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Work Shown:
In the top left corners of each matrix, in line 3, we have 2x+3 = 7 which solves to...
2x+3 = 7
2x = 7-3
2x = 4
x = 4/2
x = 2
In the bottom right corners, we have y-3 = -13 which solves to....
y-3 = -13
y = -13+3
y = -10