How can you tell if this equation is true. 1/2+3/8 =4/10=2/5
2 answers:
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Answer:
(a) The standard error is 0.0080.
(b) The margin of error is 1.6%.
(c) The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).
(d) The percentage of young people who earn high school diplomas has increased.
Step-by-step explanation:
Let <em>p</em> = proportion of young people who had earned a high school diploma.
A sample of <em>n</em> = 1400 young people are selected.
The sample proportion of young people who had earned a high school diploma is:
(a)
The standard error for the estimate of the percentage of all young people who earned a high school diploma is given by:
Compute the standard error value as follows:
Thus, the standard error for the estimate of the percentage of all young people who earned a high school diploma is 0.0080.
(b)
The margin of error for (1 - <em>α</em>)% confidence interval for population proportion is:
Compute the critical value of <em>z</em> for 95% confidence level as follows:
Compute the margin of error as follows:
Thus, the margin of error is 1.6%.
(c)
Compute the 95% confidence interval for population proportion as follows:
Thus, the 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).
(d)
To test whether the percentage of young people who earn high school diplomas has increased, the hypothesis is defined as:
<em>H₀</em>: The percentage of young people who earn high school diplomas has not increased, i.e. <em>p</em> = 0.80.
<em>Hₐ</em>: The percentage of young people who earn high school diplomas has not increased, i.e. <em>p</em> > 0.80.
Decision rule:
If the 95% confidence interval for proportions consists the null value, i.e. 0.80, then the null hypothesis will not be rejected and vice-versa.
The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).
The confidence interval does not consist the null value of <em>p</em>, i.e. 0.80.
Thus, the null hypothesis is rejected.
Hence, it can be concluded that the percentage of young people who earn high school diplomas has increased.
We need to account for both x values on either side of the length, and width.
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x
For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.
(5 + 2x)(10 + 2x) - 50 = 54
Expanding the brackets:
x = -9, or x = 3/2
Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2
Thus, the length becomes 10 + x + x = 10 + 2x
and the width becomes 5 + x + x = 5 + 2x
For the second question, I'm assuming we don't account for the area that is covered by the garden.
Then we can say that the path is measured by: (5 + 2x)(10 + 2x) - 50, which is the area of the garden itself.
(5 + 2x)(10 + 2x) - 50 = 54
Expanding the brackets:
x = -9, or x = 3/2
Since x > 0, then x ≠ -9
Thus, the only x-value we can take is x = 3/2