Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabyt
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Irrational numbers are the subset of real numbers that are not at all connected to the rest of numbers.
The subsets of real numbers are natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Natural numbers are subset of whole numbers, which are subset of integers, which are subset of rational numbers. Hence, all of them are interconnected. The set of irrational numbers is the only subset of real numbers which is not associated with the rest.
For example:-
1 is a natural number, whole number, integer, rational number but not irrational number. On the other hand, is an irrational number but none of the rest.
To learn more about real numbers, here:-
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Answer:
(a) Hence, the margin of error reported by The Marist Poll was correct.
(b) Based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Step-by-step explanation:
We are given that the Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age.
It was also reported that interviews were conducted on 1,018 American adults, and that the margin of error was 3% using a 95% confidence level.
(a) <u>Margin of error formula is given by;</u>
Margin of Error =
where, = level of significance = 1 - 0.95 = 0.05 or 5%
Standard of error =
Also, = sample proportion of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age = 66%
n = sample of American adults = 1.018
The critical value of z for level of significance of 2.5% is 1.96.
So, <em>Margin of Error </em>=
= = 0.03 or 3%
Hence, the margin of error reported by The Marist Poll was correct.
(b) Now, the pivotal quantity for 95% confidence interval for the population proportion who think that licensed drivers should be required to retake their road test once they turn 65 is given by;
P.Q. = ~ N(0,1)
So, <u>95% confidence interval for p</u> =
=
= [0.66 - 0.03 , 0.66 + 0.03]
= [0.63 , 0.69]
Hence, based on a 95% confidence interval the poll does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65 because the interval does not include the value of 70% or more.