Answer:
False
Step-by-step explanation:
(Mark me Brainliest Please .-. )
Assuming normality, construct the requested confidence interval.
A sociologist is interested in the age at which a mother has her first child. A random sample of 20 recent births yielded an average maternal age to be 30 years with a standard deviation of 6.2 years.
Construct a 99% confidence interval for the mean age at which a mother has her first child.
Can I have some help with solving this problem with a TI84 calculator?
Answer:
The appropriate response is "(26.03, 33.97)".
Step-by-step explanation:
The given values are:
Average maternal age,
[tex]\bar{x} = 30[/tex]
Standard deviation,
s = 6.2
Random sample,
n = 20
Now,
The degree of freedom will be:
⇒ [tex]df=n-1[/tex]
[tex]=20-1[/tex]
[tex]=19[/tex]
"t" at confidence level 99%, will be:
⇒ [tex]\alpha=1-99 \ percent[/tex]
[tex]=1-0.99[/tex]
[tex]=0.01[/tex]
⇒ [tex]\frac{\alpha}{2}=\frac{0.01}{2}[/tex]
[tex]=0.005[/tex]
⇒ [tex]t\frac{\alpha}{2} \ df=t \ 0.005,19[/tex]
By using the student table, we get
[tex]=2.86 1[/tex]
The margin of error will be:
⇒ [tex]E=\frac{t \alpha}{2,df\times (\frac{s}{\sqrt{n}})}[/tex]
On substituting the estimated values, we get
⇒ [tex]=2.861\times (\frac{6.2}{\sqrt{20}})[/tex]
⇒ [tex]=3.97[/tex]
At 99%, the confidence level will be:
⇒ [tex]\bar{x}-E< \mu <\bar{x}+E[/tex]
⇒ [tex]30-3.97< \mu < 30+3.97[/tex]
⇒ [tex](26.03,33.97)[/tex]
Thus the above is the correct approach.
How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?
A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.
B. What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?
Complete Question
How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?
Exercise 9.53
A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.
B. What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?
Answer:
The First question
[tex] n = 1879 [/tex]
A
The 96% confidence interval is
[tex]0.51 < p < 0.63 [/tex]
B
The possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is
[tex]E = 0.06 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.02[/tex]
The sample size is n = 200
The number that supported the annexation suit is k = 114
Considering the first question
Generally our sample in Exercise 9.53 is [tex]\^ p = 0.57[/tex]
From the question we are told the confidence level is 96% , hence the level of significance is
[tex]\alpha = (100 - 96 ) \%[/tex]
=> [tex]\alpha = 0.04[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.751 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.751}{0.02 } ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.751}{0.02 } ]^2 * 0.57 (1 -0.57 ) [/tex]
=> [tex] n = 1879 [/tex]
Considering question B
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.751 * \sqrt{\frac{ 0.57 (1- 0.57 )}{200} } [/tex]
=> [tex]E = 0.06 [/tex]
Considering question A
Generally the sample proportion of the number that supported the annexation suit is mathematically represented as
[tex]\^ p = \frac{114}{200}[/tex]
=> [tex]\^ p = 0.57[/tex]
Generally 96% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.57 - 0.06 < p < 0.57 + 0.06 [/tex]
=> [tex]0.51 < p < 0.63 [/tex]
arithmetic sequence
Answer:
First, find the common difference for the sequence. Subtract the first term from the second term. Subtract the second term from the third term. Subtract the third term from the fourth term. To find the next value, add to the last given number.
Step-by-step explanation:
Find the measure of one exterior angle of a regular octagon
Answer:
each of the eight angles measures 45 degrees
Step-by-step explanation:
The sum of all exterior angles of any polygon always measures 360 degrees.
If it's 'regular' then all angles have the same measures.
If it's an octagon, then it has 8 sides.
360 divided by 8 = 45
I think i got the answer but a second opinion would be greatly appreciated!
Answer:
Your answer would be B: 30 ft squared
Step-by-step explanation:
Find the area of the circle: 5.5 (radius) multiply it by itself then multiply that by 3.14 which gets you 94.985. Now find the area of the square which is 8*8 = 64. Subtract 64 from 94.985 and your answer will be 30.985. The questions asks for the approximate (estimate), so the closest one would be 30 ft squared
What is the type of correlation for the plot?
happy holidays! please help me, it's algebra 2!
Answer:
Answer Choice B
Step-by-step explanation:
f(x) is just another way of saying y=.
To inverse, just flip the x & y and isolate the y variable.
[tex]x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9}=y[/tex]
Divide.
8.43) 12.645
The quotient is
Answer:
1.5 or 3/2
Step-by-step explanation:
The division results the quotient is 1.5
What is Division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication. In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items.
Given:
We have to divide 12.645 by 8.43
So, 12.645/8.43
= 12645/ 8430
= 8430 | 12645 | 1 . 5
8430
-______
42150
42150
_______
0
Hence, the quotient is 1.5.
Learn more about division here:
https://brainly.com/question/21416852
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how do I find the percentage of filled seats verus non filled seats for a class
Answer:
since i dont have data this is the best i can do
Step-by-step explanation:
non-filled seats diveded by total number of seats, everything multilped by 100 gives you percentage of non-filled seats.
Filled seats diveded by total number of seats, everything multilped by 100 gives you percentage of filled seats.
total should add up to 100
Write equations for the vertical and horizontal lines passing through the point (0, -3).
Answer:
Vertical line will be x=0, and horizontal line will be y=-3
Step-by-step explanation:
Draw a vertical line through point (0,-3). You will see it's on the y-axis. The equation of the line on y-axis is always x=0, because no matter what point you choose on the line, the x coordinate will be 0. (0,-3), (0, -2), etc.
Next draw a horizontal line through (0,-3). It's parallel to the x axis, and no matter what point on the line you choose, the y coordinate will be -3. (0,-3), (1, -3), etc
The equation for the vertical line is x=8 and the horizontal line is y=−7.
The given coordinate point is (0, -3).
What are the vertical and horizontal lines?A vertical line is a line, parallel to the y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to the x-axis and goes straight, left and right.
Now,
For a vertical line the value of x, in this case, 8, will never change. This will be true for any value of y. Therefore the equation for a vertical line passing through this point is: x=8
Likewise, for a horizontal line the value of y, in this case, −7, will never change. This will be true for any value of x. Therefore the equation for a horizontal line passing through this point is: y=−7
Therefore, the equation for the vertical line is x=8 and the horizontal line is y=−7.
To learn more about the vertical and horizontal lines visit:
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Write an expression that represents the area of
the figure in square centimeters.
HELP ASAP
Answer:
its either 98 cm or 28 cm
Step-by-step explanation:
7 x 7 = 49 x 2 = 98 cm
14 x 2 = 28
If f(x)= 3^x+ 10x and g(x) = 4x-2 find (f-g)(x)
Answer:
u may need a calculator
Step-by-step explanation:
A plate moves 200 m in 10,000 years. What is its rate in cm/year? 0.02 cm/year 2 cm/year 10 cm/year 100 cm/year
Answer: 2cm/year
Step-by-step explanation:
1m = 100cm
200m = 20000cm
10,000years = 20,000cm
1 year = 20,000/10,000 = 2cm
It's rate is 2cm/year
Answer:
0.02 cm/year
Step-by-step explanation:
200m:10,000 years
10,000 divided by 10,000=1
200 divided by 10,000=0.02
0.02m : 1 year
Best,
SunflowerJada
Find the Missing Lengths is the sides.
Answer:
b
Step-by-step explanation:
Help please math people
Answer:
-12.50x+350<210
Step-by-step explanation:
Use the order of operations to simplify the following expression.
16+(14-6)x3-62-6
O 18
O None of the other answers are correct
O 78
0 34
O 12
Lisa received 34 text messages on Monday and 43 text messages on Tuesday. She received 98 text messages on Wednesday. How many more text messages did Lisa receive on Wednesday than on Monday and Tuesday combined?
Answer:
she received 21 more
Step-by-step explanation:
43 + 34 =77
98-77= 21
Hope this helps!!!
Elena uses 12 red beads to make 4 bracelets how many red beads will Elena need to make 12 bracelets ,
Part 2 :How many red beads will Elena need to make
16 bracelets?
Part 1:
Answer:36 red beads
Step-by-step explanation:
12/4=3 beads per bracelet
3x12=36 red beads
Part 2:
Answer:48 red beads
Explanation:
We know 3 red beads per bracelet.
3x16=48 red beads
Over which of the given intervals does g have an average rate of change of zero?
Choose 1 answer:
3<3<9
B
2 <3 <4
-9 <<-5
D
--2 <<3
Answer:
I think is c 2 hope that works
Step-by-step explanation:
please give brainliest :D
An adult ticket for a musical cost $12. A children's ticket for the musical cost $4. The number of adult tickets sold is 4 times the number of children's tickets sold. A total of 1560 is taken in for ticket sales.
1. 160 adult tickets and 40 children's tickets
2. 120 adult tickets and 30 children's tickets
3. 40 adult tickets and 160 children's tickets
4. 30 adult tickets and 120 children's tickets
Answer:
B
Step-by-step explanation:
multiple 12 and 120 which is 1,440 then multiply 4 and 30 which is 120 and add it up which comes to 1,560. HOPE THIS HELP!!!
The total number of adults tickets sold and children tickets sold is 120 adult tickets and 30 children's tickets
Given:
Cost of adult tickets = $12
Cost of children tickets = $4
let
number of children tickets sold = x
number of adult tickets = 4x
Total cost of tickets = 1560
The equation:
1560 = 12(4x) + 4(x)
1560 = 48x + 4x
1560 = 52x
divide both sides by 52
x= 1560/52
x = 30
Therefore,
number of children tickets sold = x
= 30 tickets
number of adult tickets = 4x
= 4(30)
= 120 tickets
Read more:
https://brainly.com/question/15165519
a. Find the slant asymptote of the graph of the rational function.
b. Follow the seven-step strategy and use the slant asymptote to graph the rational function.
a. Select the correct choice below and, if necessary, fill in the answer box to complete the choice.
A.
The equation of the slant asymptote is
nothing.
(Type an equation.)
B.
There is no slant asymptote.
Click to select and enter your answer(s) and then click Check Answer.
Answer:
BROOO I LITERALLY HAD A WHOLE LOOOONG ANSWER AND SOME STU PID MOD CAME AND DELETED IT AND I DONT REMEMBER WHAT I PUT
Step-by-step explanation:
Answer:
a. 1/3x+6
Step-by-step explanation:
what does x equal?
4x+7=31
Answer:
x = 6
Step-by-step explanation:
First, subtract 7 from both sides to get x alone. That will give you 4x = 24 .
Then divide both sides by 4 to remove the coefficient of x. That means x = 6.
4x+7=31
-7 -7
4x=24
÷4 ÷4
x = 6
Find the mean, mode, median and the range.
-4, -10, 6, 11, -16, 8, -7, 8, 34, 6
Answer:
mean:4.4
median:8
mode:8 & 6
range;50
Step-by-step explanation:
mean=sum/total
mean= -4 + -10 + 6 + 11 + -16 + 8 + -7 + 8 + 34 + 6/10
mean= 4.4
mode=most occuring number
mode= 8 & 6
median: arrange the data in ascending or descending order
median:-16,-10,-7,-4,8,8,6,6,11,34: in ascending order
median:8+8/2
median :16/2
median: 8
Range: highest value- lowest value
range:34-(-16)
range:50
Plzzzz help. Giving brainlist and 20 pts.
Answer:
The value of AC = 5 units
Step-by-step explanation:
Given the triangles
ΔABCΔXYZIn the diagram,
ΔABC ~ ΔXYZWe know that two triangles are termed as similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Therefore,
AB : XY = AC : XZ
AB / XY = AC / XZ
as
AB = 4XY = 6XZ = 7.5AC = ?so we can determine AC as the ratios of the side become
4 / 6 = AC / 7.5
AC = 4/6 × 7.5
= 5 units
Therefore, the value of AC = 5 units
If you are buying at item at a store for a price of $72, and there is a 6.2% tax added on top, what would be the total amount due at the register, to the nearest cent?
Answer:
Sale Tax($): 4.5
Step-by-step explanation:
Before Tax Price ($): 72
Tax Rate (%): 6.2
Final Price Including Tax ($): 76.46
Sale Tax($): 4.46
Answer:
76.46
Step-by-step explanation:
6th grade math proportionally
Answer:
9.
Step-by-step explanation:
A car traveled from Indianapolis, Indiana to Miami, Florida at an average rate of 70 miles per hour. The distance was 1,203 miles. About how long did the trip take?Immersive Reader
(1 Point)
About 17 hours
About 22 hours
About 24 hours
About 32 hours
Answer: About 17 hours
Step-by-step explanation:
1,203/70=17.18571429
17.18571429 is about 17 hours
Please help fast!!!! Find the seventh term of the geometric sequence if a1=7 and r=3
Answer:
15309 Im pretty sure
Step-by-step explanation:
a7=ar^7
=7(3^7)
7 x 2187=15309
Solve 4x+34 help please
9514 1404 393
Answer:
78
Step-by-step explanation:
The base (JL) is twice the length of the midline (MN), so you have ...
4x +34 = 2(5x -16)
4x +34 = 10x -32 . . . eliminate parentheses
66 = 6x . . . . . . . . add 32-4x
11 = x
Then the length of JL is ...
4(11) +34 = 78
if the probability of picking a pink jelly bean out of a bag is 4/15, what is the probability of not picking a pink jelly bean
Answer:
The probability of not picking a pink jelly bean: 11/15
Step-by-step explanation:
As we know that the maximum value of the probability of an event would always be 1.
The reason is that '1' is certain that something would happen.Given that the probability of picking a pink jelly bean out of a bag is 4/15.
Thus, the probability of not picking a pink jelly bean can be calculated by subtracting 4/15 from the maximum probability '1'.
i.e.
Probability of not picking a pink jelly bean = max probability - 4/15
= 1 - 4/15
= 11/15
Therefore, the probability of not picking a pink jelly bean: 11/15