. A National Institute of Health survey of 40467 U.S adults found that 3156 of them experienced at least one major depressive ep
1 answer:
Using the confidence interval for sample proportion formula, the C.I is (0.075; 0.081)
<u>Using</u><u> </u><u>the</u><u> </u><u>relation</u><u> </u><u>:</u>
<u></u>
- Sample size, n = 40467
- Sample proportion, p = 3156/40467 = 0.078
- Zcrit at 95% = 1.96
- Margin of Error =
- Margin of Error = 0.0026128
Lower boundary = 0.078 - 0.0026128 = 0.075
Upper boundary = 0.078 + 0.0026128 = 0.081
Hence, the confidence interval is (0.075; 0.081)
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Answer:
Answer choice D:
y - 6 = 2(x - 5)
Step-by-step explanation:
This question is basically asking you to find the point-slope form equation for a line going through the points (3, 2) and (5, 6).
As you can tell by the name, point-slope form needs both a point that the line goes through and the slope of the line.
You can find the slope of the line by using the slope formula since you have two points that the line goes through.
Slope formula:
Substitute in the points A and B into the formula.
The slope of this line is 2.
Now since we have the slope and a point of the line, we can plug this into the point-slope form equation, which is y - y1 = m(x - x1).
We will be using one of the points (I will be using point A) to substitute the coordinates into y1 and x1, and using the slope to substitute into m.
Substitute point A's coordinates and the slope of the line into the point-slope form equation.
y - (2) = 2(x - (3))
I always put parentheses around the numbers I substitute into an equation to see exactly what is being plugged in, but now you can remove them to find your answer.
y - 2 = 2(x - 3)
Now, since none of the answer choices do not fit with the answer we have found, we can use the other point coordinate-- point B.
Substitute point B and the slope 2 into the equation.
y - (6) = 2(x - (5))
Remove the parentheses.
y - 6 = 2(x - 5)
There is an answer choice for this answer we have found, answer choice D.
By the way, both of the equations we found: y - 2 = 2(x - 3) and y - 6 = 2(x - 5) will yield the same answer in the end so don't worry if one of the points don't work if you have a multiple choice like this question.
Answer:
A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].
Step-by-step explanation:
We are given that x is normally distributed with a known standard deviation of 12.6.
A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample average mean response = 9 hours
= population standard deviation = 12.6
n = sample of legal professionals = 250
= mean number of hours a legal professional works
<em>Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [7.44 hours, 10.56 hours]
Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].