Answer:
a) 16.6
b) The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c) The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d) The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.
Step-by-step explanation:
a. Find the best point of estimate of the population mean
The best estimate for the population mean is the sample mean, which is 16.6
b. Find the 95% confidence level of the mean of the time playing video games
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{2.8}{\sqrt{35}} = 0.9[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 0.9 = 15.7 hours
The upper end of the interval is the sample mean added to M. So it is 16.6 - 0.9 = 17.5 hours
The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.
c. Find the 99% confidence interval of the mean time playing video games
Following the same logic as above, we have that [tex]Z = 2.575[/tex]. So
[tex]M = 2.575\frac{2.8}{\sqrt{35}} = 0.9[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 1.2 = 15.4 hours.
The upper end of the interval is the sample mean added to M. So it is 16.6 + 1.2 = 17.8 hours.
The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.
d. Which is larger? Explain why.
The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.
The mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.
It is given that the in recent study of 35 ninth-grade students the mean number of hours per week is 16.6 with standard deviation of the population was 2.8.
It is required to find the best point of estimate of the population mean, 95% confidence interval, and 99% confidence interval.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have confidence level = 95% = 0.95
We know:
[tex]\alpha = \frac{1-0.95}{2}[/tex] = 0.025
[tex]\rm Z_1 _-_\alpha = Z_{0.975} = 1.96[/tex] (from the Z table)
The sample size n = 35
We know the Margin of error formula:
[tex]\rm M =Z\frac{\sigma}{\sqrt[]{n} }[/tex] ( [tex]\rm \sigma\\[/tex] = 2.8 )
[tex]\rm M =1.96\frac{2.8}{\sqrt[]{35} }[/tex]
M = 0.92
The 95% interval will be:
= X - M ⇒ 16.6 - 0.92 ⇒15.68
= X+ M ⇒ 16.6+0.92 ⇒ 17.52
For 99% confidence level:
[tex]\alpha = \frac{1-0.90}{2} = 0.005[/tex]
[tex]\rm Z_1 _-_\alpha = Z_{0.005} = 2.575[/tex] (from Z table)
[tex]\rm M =2.575\frac{2.8}{\sqrt[]{35} }[/tex]
M = 1.21
The 99% interval will be:
=16.6 - 1.21 ⇒ 15.39
= 16.6+ 1.21 = 17.81
As the value of M increases the confidence value increases due to the value of Z that means 99% confidence interval is larger.
Thus, the mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.
Learn more about the confidence interval here:
brainly.com/question/6654139
HELP 100 POINT FAST (NO WRONG ANSWER) + BRAINLIEST TO WHO EVER ANSWERS FIRST U^U
Answer:
[tex]\Large \boxed{\sf A}[/tex]
Step-by-step explanation:
[tex]\displaystyle \left(\frac{2}{3}\right)^4[/tex]
n → exponent, means to multiply the base number by itself n no. of times.
Here we multiply the base number by itself 4 times.
[tex]\displaystyle \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}[/tex]
Answer: A.
To expand a exponent, you'll find the number how much it powers by and expand it by what the power or exponent number represents.
The fraction is 2/3 and the exponent is 4. Like I've said before, to expand it you'll find the number how much it powers by.
In the equation, 2/3 is going to the 4th power, so we will expand the fraction 4 times.
2/3 × 2/3 × 2/3 × 2/3
is 2/3 to the 4th power in expanded form.
Hence, A is the answer.
Help&EXPLAIN
•••••••••••••••••••
Using the net below, find the surface area of the triangular prism .
Step-by-step explanation:
step 1. the surface area of this object is the addition of 3 rectangles and 2 triangles
step 2. the area of a rectangle is bh. the area of a triangle is (1/2)bh where b is the base and h is the height
step 3. 20*9 + 20*9 +20*6 + (1/2)6*8 + (1/2)6*8 assuming both triangles have h = 8
step 4. 180 + 180 + 120 + 24 + 24
step 5. answer: 528 cm^2
Which of the following statements must be true about this diagram? Check
all that apply.
A. Z>X
B. W>y
C. W >X
D. y+z= w
E. x + y = w
F. x + y = 2
Answer:
f
Step-by-step explanation:
I'm pretty sure it's f from what I know
Solve for all missing zeros
Please help 20 points!!!
Answer:
The answer is z= 1,-1+i[tex]\sqrt{6}[/tex], -1-i [tex]\sqrt{6}[/tex]
Step-by-step explanation:
-x-6+2y=0
Rewrite in slope intercept form, and show steps
Answer:
Slope intercept form: y=mx+b
-x-6+2y=0
2y=x+6
y=1/2(x+6)
y=1/2x+3
Let me know if this helps!
Step-by-step explanation:
slope intercept is y=mx+b
add -x to the other side to get
-6+2y=x
then add the -6 to get
2y=x+6 then divied by 2 to get
y=1/2x+6/ 2
then simply to get
y=1/2x+3 or y=x/2+3
please help?!??!!?????
Area of it is 54ft Kv
Volume is 27 ft cube (3)
please help meeeeeeeeeeeee
Answer:
The answer is D the last one
Hope this helped
Which expression represents the product of a number y and 4?
Answer:
y+4 because bishh that's the answer lol your welcome
which point on the number line represents the location of the value of -5.5+ 8?
Which is the Better buy?
Regular Popcorn (8cups) ($4.00)
Large Popcorn (15cups) ($6.00)
what is 52 × 3552 give solution fast???
Answer:
184,704
Step-by-step explanation:
because 52 * 3552 is 184,704
The graph represents the profit earned on the sale of boxes of cookies. What does the slope represent?
the increase or decrease in profit
Step-by-step explanation:
Answer:
the profit earned for each box of cookies sold
Step-by-step explanation:
Find the volume of the solid
The problem is in the picture!!!!!!!!!
what is the difference in length between the longest ski Trail and the shortest ski trail that the longest ski Trail is 3 1/8 the shortest ski Trail is 1 3/8
The difference in length between the longest ski trail and the shortest ski trail is 7/4.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
Length of the longest ski trail = 3 1/8 = 25/8
Length of the shortest ski trail = 1 3/8 = 11/8
Difference in length between the longest ski trail and the shortest ski trail:
= 25/8 - 11/8
= 14/8
= 7/4
Thus, the difference in length between the longest ski trail and the shortest ski trail is 7/4.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
HELP !!!! Equations with 1 no or infinite solutions
1. v=0
2. No solution
3. m=0
4. No solution
5. p= -7
6. x=5
7. -12 = - 12
8. x=5
9. 3=3
10. -32= -32
11. x=0
12. No solution
I'm sorry if anything is wrong.
Step-by-step explanation:
Ok Hold UP
HELP ASAP I DONT GET IT ITS DUE IN 14 MINS
Answer:
110.5 i think D
Step-by-step explanation:
just me doing work vvvvv
65 + 45.5 = 110.5
---
7 x 6.5
45.5
Answer:
110.5
Step-by-step explanation:
if 6 is added to a quarter of a certain number the answer is 18.
what is the number?
Answer:
48
Step-by-step explanation:
6+x/4 = 18
x/4 = 12
x= 48
Answer:
x = 48
here's your solution
=>. let the number be. X
=> now , quater of this number = X/4
=> then 6 is added to it
=> we get this. =. 6 + X/4
=> it is given that this number is equal to 18
=>. so, our final equation is 6 + X/4 = 18
=> solve , X/4 = 18 - 6
=> X/4 = 12
=>. X = 12*4
=> X = 48
hope it helps
Order the data from lest to greatest 35, 24,25,38,31,20,27
Answer:
Step-by-step explanation:
20,24,25,27,31,35,38
minimum;20
medium: 27
maximum: 38
lower quartile: 24
upper quartile:35
put numbers in number order
the first number is the minimum, the last number is the maximum. the middle number "split" is the median.
quartiles are the numbers in the middle of the data you just "split"
(so like a quarter)
i may be wrong i haven't done this in years
HELP PLS THIS IS DUE SOON
Answer:
15
Step-by-step explanation:
80 percent (calculated percentage %) of what number equals 12? Answer: 15
what is $12.56 rounded to the nearest dollar? plzz help
Answer: $13, don't just copy that answer actually try to understand it. ⬇️
Step-by-step explanation: Think of it as a number line.
$12-$12.10-$12.20-$12.30-$12.40-$12.50-$12.60-$12.70-$12.80-$12.90$13
the $12.50 is directly in the middle of $12 and $13. Lets say it $12.51 now its not directly in the middle, but more over to the $13, so then we would go up to 13$ which is the nearest dollar. If it were $12.49 then it would be closer to the $12, so we would go down to $12.
I hope this helps!
I need help with this now
You want to save $500 for a trip to Legoland you have planned in 6 months. Which inequality shows the least amount you must save each month until your trip? 6x<5006x<500 6x≤5006 x is less than or equal to 500 6x≥5006 x is greater than or equal to 500 6x>5006 x is greater than 500
Answer:
6x ≥ 500
Step-by-step explanation:
I took the test but also it means that in six months, you have to save that amount of money to get exactly or more than 500, so this would be the correct answer!
How do you do this. I am stuck
irrational number between 0 and 1
Answer:
what are u asking like a true or false thing orrr?
Step-by-step explanation:
cause if so it's true
a typical tip in a restaurant is 15% of the total bill. if the bull is $160, what would the typical tip be?
Answer:
$24
Step-by-step explanation:
Fist, you will multiply the percent, 15, and the total money amount, 160, which you would get 2,400. Then, divide 2,400 by 100, and there you will get the tip, $24. I hope this helps :)
what is the value of x and what type of angle is it ?
Answer:
This is called a supplementary angle. x = 12°
And for extra credit:
y is a vertical angle to 60° and a supplementary angle to x so
y = 60°
Step-by-step explanation:
What is the area of half circle with a radius of 40 cm?
PLEASE HELPPP ILL GIVE BRAINLIEST
Answer:
0.5027 square meters
Step-by-step explanation:
cm2
Is - 4x + 5 > 25 true when x is 0? What about when x is 7? What about when x is -7?
Step-by-step explanation:
when 0: 5 > 25 = false
when 7: -28 + 5 > 25 = -23 > 25 = false
when -7: 28 + 5 > 25 = 33 > 25 = true
A point giver? This is fake. Gets 50 points. Me: ...
Answer:
thxs
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
I need help please.