A poll was taken of 588 residents in a county. The residents sampled were asked whether they think their local government did a
good job overall. 490 responded ""yes"". Let p denote the proportion of all residents in that county who think their local government did a good job. Construct a 95% confidence interval for p: Round off to two decimal places.
1 answer:
Answer:
[472.29, 507.71]
Step-by-step explanation:
The proportion is
490/588 = 0.8333
The mean can be estimated as
= 490
and the standard deviation can be approximated with
= 9.037
and we just need to find two values a and b such that the area under the Normal curve of mean 490 and standard deviation 9.037 between a and b equals 95% = 0.95
<h3>(See picture)</h3>With the help of a spreadsheet we can easily find these values which are
a = 472.288
b = 507.712
and the interval we are looking for, rounded to 2 decimals, is [472.29, 507.71]
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Answer:
The population of the small community, 5 years into the future, after the initial 20-year period = 4268.
Step-by-step explanation:
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
The exponential function will look like
p = aeᵏᵗ
where a and k are constants.
Take the natural logarithms of both sides
In p = In aeᵏᵗ
In p = In a + In eᵏᵗ
In p = In a + kt
In p = kt + In a.
We then use linear regression to fit the data of In p against t to obtain k and In a.
t | 0 | 5 | 10 | 15 | 20
p | 100 | 200 | 450 | 950 | 2000
In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601
In p = kt + In a.
y = mx + b
m = k and b = In a
Performing a linear regression analysis on the now-linear relationship between In p and t and also plotting a graph of the variables.
The regression equation obtained is
y = 0.151x + 4.584
The first attached image shows the equations necessary for the estimation of the linear regression parameters.
The second attached image shows the use of regression calculator and the plot of the function In p versus t.
Comparing
y = 0.151x + 4.584
With
In p = kt + In a.
y = In p
k = 0.151
x = t
In a = 4.584
a = 97.905
The exponential function relating p and t,
p = aeᵏᵗ now becomes
p = 97.905 e⁰•¹⁵¹ᵗ
So, to predict the population 5 years into the future, that is 5 years after the 20 year period.
we need p at t=25 years.
0.151 × 25 = 3.775
p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41 = 4268.
Hope this Helps!!!
Circumcenter and circumcirle are shown in the attachment. Assume that the triangle is DEF instead of ABC and that the intersection of perpendiculars is H.
The definition of the circumcenter of a triangle is defined as the point of intersection of all the perpendicular bisectors in the triangle.
The circumcircle passes by all three of the triangle's vertices.
Based on the above, the right choiceS will be:
Point H is the center of the circle that passes through points D, E, and F.
HD = HE
The definition of the circumcenter of a triangle is defined as the point of intersection of all the perpendicular bisectors in the triangle.
The circumcircle passes by all three of the triangle's vertices.
Based on the above, the right choiceS will be:
Point H is the center of the circle that passes through points D, E, and F.
HD = HE
Answer:
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Know that the probability frequency is:
