Jackson uses the Fermi process to estimate the number of buckets of gravel he could store in a warehouse. The buckets are shaped
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.
Answer:
1st option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = 2x + 1 ( subtract 1 from both sides )
y - 1 = 2x ( divide both sides by 2 )
= x
Change y back into terms of x with x being the inverse h(x)
h(x) = =
x -