Answer:
b
Step-by-step explanation:
In general
Given
y = f(x) then y = f(Cx) is a horizontal stretch/ compression in the x- direction
• If C > 1 then compression
• If 0 < C < 1 then stretch
Consider corresponding points on the 2 graphs
(2, 2 ) → (4, 2 )
(4, - 2 ) → (8, - 2 )
Indicating a stretch in the x- direction.
y = f( ) with C =
, that is 0 < C < 1
stretches the graph in the x- direction by a factor of 2
Thus
y = f( ) → b
Answer:
a. The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.
b. Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.
This means that
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.
(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?
Yes, because the confidence interval is entirely above 0.5.
Because this confidence interval is entirely above 0.5, the interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.