Answer:
B
Step-by-step explanation:
The term in the () is usually the x coordinate, and the last term (-1) is usually the y coordinate.
Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 48 students. The mean of the sample is 12.4 units. The sample has a standard deviation of 1.7 units.
Required:
What is the 95% confidence interval for the average number of units that students in their college are enrolled in?
Answer:
[11.906 ; 12.894]
Step-by-step explanation:
Given :
Sample mean, xbar = 12.4
Sample standard deviation, s = 1.7
Sample size, n = 48
We use the T distribution since we are using the sample standard deviation;
α - level = 95% ; df = n - 1 = 48 - 1 = 47
Tcritical = T(1 - α/2), 47 = 2.012
Using the confidence interval for one sample mean
Xbar ± Tcritical * s/√n
12.4 ± (2.012 * 1.7/√48)
12.4 ± 0.4936922
C. I = [11.906 ; 12.894]
(x - 7)2 = x2 - 49
O True
O False
Answer:
False
Step-by-step explanation:
what is 5 2/3 - 11 1/6
Answer:
Check the photo for the answer
Find the median of the following number 40,30,32,39,34,35,35,37
Terms given
40,35,32,39,34,35,35,37No of terms=8
We know
[tex]\boxed{\sf Mean=\dfrac{Sum\;of\:terms}{No\;of\:terms}}[/tex]
[tex]\\ \sf\longmapsto Mean=\dfrac{40+35+32+39+34+35+35+37}{8}[/tex]
[tex]\\ \sf\longmapsto Mean=\dfrac{270}{8}[/tex]
[tex]\\ \sf\longmapsto Mean=35[/tex]
Final Answer:
35
Step-by-step explanation:
-median is the middle number in the data set-
arrange the data set from least to greatest:
40, 30, 32, 39, 34, 35, 35, 37 ⇒ 30, 32, 34, 35, 35, 37, 39, 40
we start from the lowest number and the highest number and work your way to the middle:
30, 32, 34, 35, 35, 37, 39, 40
notice that there is no middle number:
30, 32, 34, 35, ?, 35, 37, 39, 40
so what we do is add both 35's and then divide it by 2
35 + 35 = 70 ÷ 2 = 35
median: 35
Which line segment has the same measure as ST?
RX
TX
SR
XS
Answer:
The answer is Line Segment SR.
five sutracted from x is at most -21 translate the sentence into an inequality?
Complete the statement below. A Type II Error is made... Choose the correct answer below. A. A Type II Error is made when there's not enough evidence to reject the null hypothesis and the null hypothesis is true. B. A Type II Error is made when there's evidence to reject the null hypothesis, but the null hypothesis is true. C. A Type II Error is made when there's not enough evidence to reject the null hypothesis, but the null hypothesis is not true. D. A Type II Error is made anytime we do not reject the null hypothesis.
A sample of 42 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 101.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.6. The sample mean is 99.0. Conduct the following test of hypothesis using the 0.04 significance level.
H0 : μ1 = μ2
H1 : μ1 ≠ μ2
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding H0?
d. What is the p-value?
Answer:
a)
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b) [tex]z = 2.81[/tex]
c) Reject.
d) The p-value is 0.005.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Population 1:
Sample of 42, standard deviation of 3.3, mean of 101, so:
[tex]\mu_1 = 101[/tex]
[tex]s_1 = \frac{3.3}{\sqrt{42}} = 0.51[/tex]
Population 2:
Sample of 53, standard deviation of 3.6, mean of 99, so:
[tex]\mu_2 = 99[/tex]
[tex]s_2 = \frac{3.6}{\sqrt{53}} = 0.495[/tex]
H0 : μ1 = μ2
Can also be written as:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
H1 : μ1 ≠ μ2
Can also be written as:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error .
a. State the decision rule.
0.04 significance level.
Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b. Compute the value of the test statistic.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = \mu_1 - \mu_2 = 101 - 99 = 2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.51^2 + 0.495^2} = 0.71[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{2 - 0}{0.71}[/tex]
[tex]z = 2.81[/tex]
c. What is your decision regarding H0?
[tex]|z| = 2.81 > 2.054[/tex], which means that the decision is to reject the null hypothesis.
d. What is the p-value?
Probability that the means differ by at least 2, either plus or minus, which is P(|z| > 2.81), which is 2 multiplied by the p-value of z = -2.81.
Looking at the z-table, z = -2.81 has a p-value of 0.0025.
2*0.0025 = 0.005
The p-value is 0.005.
The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
What percentage of young adults send between 68 and 158 text messages per day?
34%
47.5%
81.5%
95%
This value is approximate.
====================================================
Explanation:
We have a normal distribution with these parameters
mu = 128 = population meansigma = 30 = population standard deviationThe goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).
Let's convert the score x = 68 to its corresponding z score
z = (x-mu)/sigma
z = (68-128)/30
z = -60/30
z = -2
This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.
Repeat for x = 158
z = (x-mu)/sigma
z = (158-128)/30
z = 30/30
z = 1
This value is exactly one standard deviation above the mean
-------------------------------------------
The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)
We do this because we can then use the Empirical rule as shown in the diagram below.
We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%
Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.
Answer:
C. 81.5%
Step-by-step explanation:
Which equation represents the data in
the table?
x 0 1 2 3 4
y -4 -2 0 2 4
F y= x -4
G y= 2x -2
H y = 2x - 4
I y= 4x -4
Answer:
y = 2x - 4
Step-by-step explanation:
The equations are put in slope intercept form
Slope intercept form: y = mx + b
Where m = slope and b = y intersect
So in order to find the equation of the data represented by the table we will have to find the slope and y intercept
Let's begin!
First let's find the slope
We can find the slope by using the slope formula
m = (y2 - y1) / (x2 - x1) where the x and y values are derived from coordinates from the table
The points chosen may vary but I have chosen the points (0,-4) and (1,-2)
Now that we have chosen the points we will use to find the slope let's define the variables
remember coordinates are written like this: (x,y)
The x value of the second coordinate is 1 so x2 = 1
The x value of the first coordinate is 0
So x1 = 0
The y value of the second coordinate is -2 so y2 = -2
The y value of the first coordinate is -4
So y1 = -4
Now that we have defined each variable let's plug in the values into the formula
Formula: m = (y2 - y1) / (x2 - x1)
Variables: x2 = 1, x1 = 0, y2 = -2, y1 = -4
Substitute values
m = (-2 - (-4) / ( 1 - 0 )
Evaluate
The negative signs cancel out on top and it changes to +4
m = (-2 + 4)/(1-0)
Add top values
m = 2/(1-0)
Subtract bottom numbers
m = 2/1
Simplify fraction
m = 2
So we can conclude that the slope (m) = 2
Now let's find the y intercept or "b"
The y intercept is the value of y when x = 0
If you look at the table when x = 0 y = -4 meaning that the y intercept or "b" is -4
Now that we have found everything let's find the equation of the data represented by the table
The equation is in slope intercept form
y = mx + b
Define variables
m = 2 and b = -4
Substitute values
y = 2x - 4
The equation is y = 2x - 4
Eli had mini-golf scores of -3, -4, and -3. What was his total score for the three rounds?
Answer:-10
-3+-4+-3
-3-4=-7
-7+-3=-7-3
=-10
Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.)
Round your answer to two places, where applicable.
Side AB 3 Side BC 4 Side AC ?
Answer:
side AC is 5
Step-by-step explanation:
by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.
AB =3 BC=4
9+16=25
25 square root is 5
makeing AC=5
Working for a car company, you have been assigned to find the average miles per gallon (mpg) for acertain model of car. you take a random sample of 15 cars of the assigned model. based on previous evidence and a qq plot, you have reason to believe that the gas mileage is normally distributed. you find that the sample average miles per gallon is around 26.7 with a standard deviation of 6.2 mpg.
a. Construct and interpret a 95% condence interval for the mean mpg, , for the certain model of car.
b. What would happen to the interval if you increased the condence level from 95% to 99%? Explain
c. The lead engineer is not happy with the interval you contructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Answer:
a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c) 37 cars would have to be sampled.
Step-by-step explanation:
Question a:
We have the sample standard deviation, and thus, the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.
The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.
The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain
Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.
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 Z-table as such z has a p-value 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.
How many cars would you have to sample to create the interval the engineer is requesting?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*6.2[/tex]
[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]
[tex]n = 36.9[/tex]
Rounding up:
37 cars would have to be sampled.
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
-6
Step-by-step explanation:
f(x) = -2x - 7 and g(x) = -4x + 6
Find f(-5)
f(-5) = -2(-5) -7 = 10-7 = 3
The find g(3)
g(3) = -4(3) +6
= -12 +6 =-6
g(f(-5)) = -6
Help I have a time limit
Answer:
I think its C:37
Step-by-step explanation:
And if im wrong sorry :/
Political Stcibility
Answer:
Political stability is a variable of great importance in a country's evolution since, across time, it was identified as causing law level of economic growth, but also it was presented as a consequence of poor economic development.
Find first derivative of f(x)=(x+1)(2x-1)
Answer:
[tex]4x-1[/tex]
Step-by-step explanation:
i need help asap !!!
If Logx (1 / 8) = - 3 / 2, then x is equal to what?
Answer:
Logx(1/8) = -3/2
x = 4
Answered by GAUTHMATH
A turboprop plane flying with the wind flew 1,200 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air.
Answer:
30 and 270 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*4=1200 and (x-y)*5=1200. Solving it, we get x=270 and y=30
Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is not enough evidence to support the claim that the bags are under filled.
Step-by-step explanation:
Given :
Population mean, μ = 433
Sample size, n = 26
xbar = 427
Variance, s² = 324 ; Standard deviation, s = √324 = 18
The hypothesis :
H0 : μ = 433
H0 : μ < 433
The test statistic :
(xbar - μ) ÷ (s/√(n))
(427 - 433) / (18 / √26)
-6 / 3.5300904
T = -1.70
The Pvalue :
df = 26-1 = 25 ; α = 0.05
Pvalue = 0.0508
Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled
What is the range of this data: 42,20,36,51,60,28
Answer:
40
Step-by-step explanation:
range is the difference between the highest and lowest number.
60 is the highest and 20 is the lowest
60-20=40
A hexagonal pyramid is located ontop of a hexagonal prism. How many faces are there?
A. 15
B. 24
C. 6
D. 13
Answer:
15
Step-by-step explanation:
The figure has total 15 faces, the correct option is A.
What is a Hexagon?A hexagon is a polygon with six sides.
A hexagonal pyramid has 8 faces
From (2 hexagonal base + 6 lateral surfaces)
A hexagonal prism has 7 faces
From ( A hexagonal base + 6 lateral faces)
Total faces the figure has is 8 +7 = 15
To know more about Hexagon
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pls help
Drag each tile to the correct location on the inequality. Each tile can be used more than once.
Consider the graphed function.
y2
8
-6
H4
+2
-6
-4
-2
2
4
6
8
-2
-6
8
What are the domain and the range of this function?
-5
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The given graph is a line and he line is the distance between two points. The required equation of the line is y = 0.5x + 5
Inequality graphThe given graph is a line and he line is the distance between two points. The equation of a line is represented as;
y = mx+ b
m is the slopeb is the interceptGiven the coordinate points (-5, 4) and (1, 7)
Get the slope
Slope = 7-4/1-(-5)
Slope = 3/6
Slope = 0.5
The intercept is 5 (the point where the line cuts the y-axis)
Determine the required equation
y = 0.5x + 5
Hence the required equation of the line is y = 0.5x + 5
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Find HG and HI.
A. HG = 11/ square root 3 and HI = 7 square root 3
B. HG= 11 square root 3/3 and HI= 7 square root 3/3
C. HG= 11 square root 3 and HI = 23 square root 3
D. HG= 11 square root 3/3 and HI = 22 square root 3/3
Answer: Choice D
HG= 11 square root 3/3 and HI = 22 square root 3/3
In other words, [tex]\text{HG} = \frac{11\sqrt{3}}{3} \ \text{ and } \ \text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]
==========================================================
Explanation:
Let's say that x is the short leg and y is the long leg
For any 30-60-90 triangle, we have this connection: [tex]y = x\sqrt{3}[/tex]
The long leg y is exactly sqrt(3) times longer compared to the short leg x.
Let's solve for x and then plug in y = 11
[tex]y = x\sqrt{3}\\\\x = \frac{y}{\sqrt{3}}\\\\x = \frac{y*\sqrt{3}}{\sqrt{3}*\sqrt{3}}\\\\x = \frac{y\sqrt{3}}{3}\\\\x = \frac{11\sqrt{3}}{3}\\\\[/tex]
Side HG, the shorter leg, has an exact length of [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex]
------------------
Once we know the short leg, we double that expression to get the length of the hypotenuse. Like before, this only applies to 30-60-90 triangles.
[tex]\text{hypotenuse} = 2*(\text{short leg})\\\\\text{HI} = 2*\text{HG}\\\\\text{HI} = 2*\frac{11\sqrt{3}}{3}\\\\\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex]
------------------
Since [tex]\text{HG} = \frac{11\sqrt{3}}{3}\\\\[/tex] and [tex]\text{HI} = \frac{22\sqrt{3}}{3}\\\\[/tex], this shows that choice D is the final answer.
18 is 65% of what number
Answer:
65% of 27.69 is 18.
Step-by-step explanation:
Formula = Number x 100
Percent = 18 x 100
65 = 27.69
Following shows the steps on how to derive this formula
Step 1: If 65% of a number is 18, then what is 100% of that number? Setup the equation.
18
65% = Y
100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
65Y = 18 x 100
65Y = 1800
Y = 1800
100 = 27.69
Calculate the GPA of a student with the following grades: B (77 hours), D (66 hours), F (2020 hours). Note that an A is equivalent to 4.04.0, a B is equivalent to a 3.03.0, a C is equivalent to a 2.02.0, a D is equivalent to a 1.01.0, and an F is equivalent to a 00. Round your answer to two decimal places.
Answer:
The student's GPA is of 0.82.
Step-by-step explanation:
GPA:
To find the student's GPA, we find his weighed mean.
Grades:
7 hours worth 3(B)
6 hours worth 1(D)
20 hours worth 0(F). So
[tex]M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82[/tex]
The student's GPA is of 0.82.
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
The triangles are similar. Find x.
Please help me!
GIVEN -> Triangles r similar
so sides r in ratio
[tex] \frac{2.4}{3} = \frac{2.8}{x} \\ 0.8 = \frac{2.8}{x} \\ x = \frac{2.8}{0.8} \\ x = \frac{28}{8} \\ x = 3.5 \: \: ans[/tex]
Answer:
3.5
Step-by-step explanation:
We can write a ratio to solve
2.4 2.8
----- = --------
3 x
Using cross products
2.4x = 3(2.8)
2.4x =8.4
Divide each side by 2.4
2.4x /2.4 = 8.4/2.4
x = 3.5
Find the missing segment in the image below
Answer:
The missing segment length is 20.
Step-by-step explanation:
2 is multiplied by 4 to get to 8, so 5 must be multiplied by 4 to get to 20.
