One moving company charges $800 plus $16 per hour. another moving company charges $720 plus $21 per hour. at what number of hour
1 answer:
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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.
A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write .
Per price increase is $20. So four price increase is $. Hence, price per dive is 100+80=$180.
Also per price increase, 2 customers are reduced from 30. For 4 price increases, customers are reduced. Hence, total customers is
.
So Total Revenue is:
B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.
Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.
Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.
C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as , where a is the coefficient of
and b is the coefficient of x. So we have,
That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be . So the price that gives the greatest revenue is
.
ANSWERS:
A. $3960
B.
C. $200