If you are selecting courses for next semester and you have 4 options to fill your science requirement, 2 options to fill your d
1 answer:
Answer: 160
Step-by-step explanation:
Given : The options to fill science requirement =4
The options to fill diversity requirement =2
The options to fill English requirement =5
The options to fill math requirement = 4
The Fundamental Counting Principle say that the number of total outcomes is equal to the product of the number of ways of all the events occur in the problem.
Using Fundamental Counting Principle, we have the total number of possible outcomes for the given situation :-
Hence, the total number of possible outcomes = 160
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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.