Answer:
a) In the step-by-step explanation.
b) The null and alternative hypothesis are:
[tex]H_0: \mu=125000\\\\H_a:\mu> 125000[/tex]
c) P-value = 0.015
d) The conclusion, at a level of significance of 0.05, is that there is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.
e) The claim of the chamber of commerce is false. We have statistical evidence against that claim and we can conclude that the mean prices are significantly higher than $125,000.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim, expressed in the alternative hypothesis, is that area residential property is available at a mean cost significantly higher than $125,000 per lot.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=125000\\\\H_a:\mu> 125000[/tex]
The significance level is 0.05.
The sample has a size n=32.
The sample mean is M=130000.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12500.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12500}{\sqrt{32}}=2209.71[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{130000-125000}{2209.71}=\dfrac{5000}{2209.71}=2.26[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=32-1=31[/tex]
This test is a right-tailed test, with 31 degrees of freedom and t=2.26, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>2.26)=0.015[/tex]
As the P-value (0.015) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 One-fourth(4x – 8y = 12) → x – 2y = 3 2x = 18 What is the solution of the system of equations? a(1,2) b(3,9) c(5,5) d(9,3)
Answer:
D
Step-by-step explanation:
because i took the test
Answer:
Option D: (9,3)
Step-by-step explanation:
Determine the place value of the digit 4 in the number 12.0764
Answer:
ten-thousandths place
Step-by-step explanation:
You start by going to the right side of the decimal. The order is tenths, hundredths, thousandths, ten-thousandths.
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two tailed, left tailed, or right tailed. The mean local monthly bill for cell phone users in this country was $47.79 in 2001. A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
This is a left tailed test.
Step-by-step explanation:
A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.
The null hypothesis will state that the monthly bill does not differ significantly from $47.79.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.
What is Three-fourths divided by one-half?
Answer:
3/2
Step-by-step explanation:
(3/4) / (1/2) is equivalent to (3/4)*(2/1), or 6/4, or 3/2.
To divide by a fraction, invert the fraction and multiply instead.
Answer:
the answer is 1 and 1/2
Find the arc length AB
Answer :
34.56
I hope it helps
Mackenzie investigated the relationship between the number of hours studying and the test score for some of the students in her class. She constructed the scatterplot below.Which statement is correct based on the scatterplot?
Answer: there is a relationship between study hours and test score. as the hours of studying increase, the test scores increase.
Answer:
C) There is a relationship between study hours and test score. As the hours of studying increase, the test scores increase.
Step-by-step explanation:
In the scatter plot, I can see that when the hours increase, so does the test scores. Thus, the answer is C
Explain how you could use the strategy solve a simpler problem to solve the equation 3/4x=3/10
Answer:
x = 0.4
Step-by-step explanation:
Let me rewrite it so it looks better:
[tex]\frac{3}{4} x=\frac{3}{10}[/tex]
The first way is to cross multiply.
30x = 12
x=0.4
The other way is to see that the two numerators are the same except for the x on the left side.
You can see the the denominators are 4 and 10.
You can create a proportion of 4 : 10 and apply it to the fractions.
You get that you have to multiply the left side by 0.4, so x = 0.4
Answer:
0.4
Step-by-step explanation:
You are planning a sample survey that involves selecting 11 of the 100 counties in North Carolina. Your sample will be a stratified sample consisting of the 6 most populous counties in the state and 5 counties randomly selected from the remaining 94 counties. Obtain your stratified sample from the US Census Bureau North Carolina county populations in this Excel file. The Excel worksheet has an alphabetical listing of all 100 North Carolina counties in column A and population estimates for July 1, 2011 and July 1, 2012 in columns D and E, respectively. We will use the population values for July 1, 2012 in column E. To simplify the selection of the 11 counties, we will order the counties according to their July 1, 2012 populations.Order the counties by July 1, 2012 population as follows:
Excel 2003
highlight the cell range A5:E105
in the Excel menu bar click on "Data"; in the drop-down menu click "Sort"
near the bottom of the Sort dialogue box click the radio button next to "Header row"
in the first "Sort by" window choose "2012" and make sure that the "Ascending" radio button is selected
click OK
Excel 2010 and Excel 2007
highlight the cell range A5:E105
Click the "Home" tab at the upper left of the Excel window
at the far right of the menu ribbon click on the "Sort and Filter" icon
In the drop-down menu click on "Custom Sort..."
In the upper right-hand corner of the Sort window make sure the box next to "My data has headers" has a check mark; if it does not have a check mark, click in the box to make a check mark appear.
In the Sort window, under Column, sort by "2012"
In the Sort window, under Sort On, choose "values"
In the Sort window, under Order, choose "A to Z"
Click OKThe counties should now be listed in increasing order according to their July 1, 2012 populations. Tyrell County should be listed first (in row 6) with July 1, 2012 population 4,338.
Question 1. Scroll down to the bottom of the worksheet to see the most populous counties. List below the 6 most populous counties and their populations. List the most populous county first and use commas in your population answers.
Answer: The answer is given below
Step-by-step explanation:
In statistics, a stratified sampling is a method of sampling that is gotten from a population that can be divided into subpopulations.
Based on th information provided in n the question, the 6 most populous counties and their populations are provided below
Mecklenburg County, North Carolina 969,031
Wake County, North Carolina 952,151
Guilford County, North Carolina 500,879
Forsyth County, North Carolina 358,137
Cumberland County, North Carolina 324,049
Durham County, North Carolina 279,64
If f(x) = 6x - 4, what is f(x) when x = 8?
2.
16
044
52
Answer:
44
Step-by-step explanation:
f(x) = 6x - 4
f(8) = 6(8) - 4
f(8) = 48 - 4
f(8)= 44
y = mx + b is the slope-intercept form of a linear equation where m = slope and b = y-intercept.
Ax + By = C is the standard form of a linear equation.
Which expression gives the y-intercept of the line when the equation is in standard form?
A.-c/b
b.c/-b
c.c/a
d.c/b
Answer:
C/B
Step-by-step explanation:
Ax + By = C
Subtract Ax from each side
Ax -Ax+ By =-Ax+ C
By = -Ax +C
Divide each side by B
By/B = -A/Bx +C/B
y = -A/Bx +C/B
The y intercept is C/B
Matt paid $6.65 to download 7 song . What is the unit rate
Answer:
$0.95 per song.
Step-by-step explanation:
If it is $6.65 for 7 songs, divide that cost by the number of songs and you get the unit rate. Hope this helps!
A basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. Mark randomly chooses a piece of fruit, eats it, then selects another. Find P(a green apple then a nectarine)
Answer:
3.17% probability of selecting first a green apple and then a nectarine.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
P(a green apple then a nectarine)
This is the probability of selecting first a green apple and then a nectarine.
Initially, there are 8+11+5+12 = 36 fruits, of which 8 are green apples. So 8/36 probability of choosing a green apple.
Now, there are 35 fruits, of which five are nectarines. So 5/35 probability of choosing a nectarine.
Then
[tex]p = \frac{8}{36}\times\frac{5}{35} = 0.0317[/tex]
3.17% probability of selecting first a green apple and then a nectarine.
Answer:
Step-by-step explanation:
(-3)^(-2) please help
Please answer this correctly
Answer:
20.7 miles
Step-by-step explanation:
[tex]2(5.4)+2t=52.2 \\\\10.8+2t=52.2 \\\\2t=41.4 \\\\t=20.7[/tex]
Hope this helps!
Given:
Breadth = 5.4 milesLength = tPerimeter = 52.2 milesTo find out:
Find the value of t ?
Formula used:
Perimeter = 2 ( length + Breadth )
Solution:
We know that,
Perimeter = 2 ( length + Breadth )
☆ Substituting the values in the above formula,we get
=> 52.2 = 2 ( 5.4 + t )
=> 52.2 = 10.8 + 2t
=> 2t = 52.2 - 10.8
=> 2t = 41.4
=> t = 41.4/2
=> t = 20.7
Suppose a researcher is estimating the proportion of trees showing signs of disease in a local forest. They randomly sample 150 trees and find that 25 of them show signs of disease. Calculate the 95% confidence interval for p, the proportion of all trees in the forest showing signs of disease.
Answer:
[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]
[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]
And the 95% confidence interval would be given (0.107;0.227).
Step-by-step explanation:
Information given
[tex]X= 25[/tex] number of trees with signs of disease
[tex] n= 150[/tex] the sample selected
[tex]\hat p=\frac{25}{150}= 0.167[/tex] the proportion of trees with signs of disease
The confidence interval for the true proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 95% confidence interval the significance is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], and the critical value would be
[tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]
[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]
And the 95% confidence interval would be given (0.107;0.227).
The value of homes sold in Hampton VA are normally distributed with a mean of $200,000
and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would
have a value greater than one standard deviation above the mean?
Answer:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
Step-by-step explanation:
Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
The position function of a particle moving along a coordinate line is given, wheresis in feet andtis in seconds.
s(t)= t/t^2+4, t>=0
a. Find the velocity and acceleration functions.
b. Find the position, velocity, speed, and acceleration at time t=1.
c. At what times is the particle stopped?
d. When is the particle speeding up? Slowing down?
e. Find the total distance traveled by the particle from time t=0 to time t=5
Answer:
a) s = (4-t)/(t^2+4)^2, a(t) = (2t^3-24t)/(t^2+4)^3
b) s = 0.2ft, v = 0.12 ft/s, a = -0.176 ft/s^2
c) t = 2s
d) slowing down for t < 2, speeding up for t > 2
e) 0.327 ft
Step-by-step explanation:
The position function of a particle is given by:
[tex]s(t)=\frac{t}{t^2+4},\ \ \ t\geq 0[/tex] (1)
a) The velocity function is the derivative, in time, of the position function:
[tex]v(t)=\frac{ds}{dt}=\frac{(1)(t^2+4)-t(2t)}{(t^2+4)^2}=\frac{4-t^2}{(t^2+4)^2}[/tex] (2)
The acceleration is the derivative of the velocity:
[tex]a(t)=\frac{dv}{dt}=\frac{(-2t)(t^2+4t)^2-(4-t^2)2(t^2+4)(2t)}{(t^2+4)^4}\\\\a(t)=\frac{(-2t)(t^2+4)-4t(4-t^2)}{(t^2+4)^3}=\frac{2t^3-24t}{(t^2+4)^3}[/tex] (3)
b) For t = 1 you have:
[tex]s(1)=\frac{1}{1+4}=0.2\ ft\\\\v(1)=\frac{4-1}{(1+4)^2}=0.12\frac{ft}{s}\\\\a(1)=\frac{2-24}{(1+4)^3}=-0.176\frac{ft}{s^2}[/tex]
c) The particle stops for v(t)=0. Then you equal equation (2) to zero ans solve the equation for t:
[tex]v(t)=\frac{4-t^2}{(t^2+4)^2}=0\\\\4-t^2=0\\\\t=2[/tex]
For t = 2s the particle stops.
d) The second derivative evaluated in t=2 give us the concavity of the position function.
[tex]\frac{d^2s}{dt^2}=a(2)=\frac{2(2)^3-24(2)}{(2^2+4)^3}=-0.062<0[/tex]
Then, the concavity of the position function is negative. For t=2 there is a maximum. Before t=2 the particle is slowing down and after t=2 the particle is speeding up.
e) Due to particle goes and come back. You first calculate s for t=2, then calculate for t=5.
[tex]s(2)=\frac{2}{2^2+4}=0.25\ ft[/tex]
[tex]s(5)=\frac{5}{5^2+4}=0.172\ ft[/tex]
The particle travels 0.25 in the first 2 seconds. In the following three second the particle comes back to the 0.172\ ft. Then, in the second trajectory the particle travels:
0.25 - 0.127 = 0.077 ft
The total distance is the sum of the distance of the two trajectories:
s_total = 0.25 ft + 0.077 ft = 0.327 ft
Identify the correct box-and-whisker plot of the given data. Then identify the interquartile range.
{6, 8, 12, 5, 3, 11, 7, 1, 6} PLEASE HELP
Answer:
Interquartile range IQR = 5.5
Step-by-step explanation:
Interquartile range IQR = third quartile Q3 - first quartile Q1
IQR = Q3 - Q1 ........1
arranging the data in ascending order;
1,3,5,6,6,7,8,11,12
The median of the data is the 5th number which is 6
Separating the data into two halves;
(1,3,5,6,),6,(7,8,11,12)
The first quartile Q1 is; (the median of the first half)
Q1 = (3+5)/2 = 4
The third quartile Q3 is; (the median of the second half)
Q3 = (8+11)/2 = 9.5
The interquartile range IQR can be derived using equation 1;
IQR = Q3 - Q1 = 9.5 - 4
IQR = 5.5
A coat manufacturer puts 431 coats in a shipment. If they sent out 80 shipments, how many coats would they have sent out?
Answer:
80 shipments will be 80 * 431 = 34,480 coats.
4. Calculate the volume of material used in making 100 ft of 4-in. type M, copper tubing.
Answer:
1443.3 in³ or 0.835 ft³
Step-by-step explanation:
Let's begin by listing out the given variables:
length (l) = 100 ft = 1200 in, nominal size = 4 in
From the copper tube of industry standard guide of the design and the installation of piping system, the dimension and physical characteristics of type M copper tubing of nominal size 4 inch is given as
Outer diameter (Do) = 4.125 in ⇒ ro = Do ÷ 2 = 2.0625 in, Inner diameter (Di) = 3.935 in ⇒ ri = Di ÷ 2 = 1.9675 in
calculate the volume of the pipe, we use the formula
V = π(ro² - ri²) * l
V = π(2.0625² - 1.9675²) * 1200
V = 1443.3 in³ or 0.835 ft³
Evaluate the expression y-x+ z for x = 4.6, y=6, and z=0.59
y - X+2=
(Type an integer or a decimal.)
Answer:
1.99Solution,
y-x+z
=6-4.6+0.59
=6+0.59-4.6
=6.59-4.6
=1.99
Hope this helps...
good luck on your assignment
The ideal mass for a piece of chocolate is 2.5 ounces. The actual mass for a production can vary by, at most, 0.08
ounces. Create an absolute value inequality and solve it to determine the range of chocolate masses.
9514 1404 393
Answer:
|m-2.5| ≤ 0.08
2.42 ≤ m ≤ 2.58
Step-by-step explanation:
The equation of interest is the one that says the positive difference from the ideal mass is at most 0.08 ounces:
|m -2.5| ≤ 0.08 . . . an absolute value inequality
The solution is found by solving the equivalent compound inequality:
-0.08 ≤ m -2.5 ≤ 0.08
2.42 ≤ m ≤ 2.58 . . . . the range of masses
Find the least common denominator for these fractions. 5/7 and 4/6
Answer: 21 is the least common denominator
Step-by-step explanation:
The least common denominator of 7 and 6 is 42, but will be simplified.
The fractions would turn into 30/42 and 28/42.
Now simplify.
15/21 and 14/21
This cannot be simplified any further without losing the common denominator
Answer:
The least common denominator is 21.
Step-by-step explanation:
Put the fractions out of a denominator of 42
5/7 = 30/42 4/6 = 28/42
Divide both fractions by 2
35/42 = 15/21 4/6 = 14/21
Johnson has recently open his workshop at the main street of a major city in the North East. Johnson estimates about 20 cars arriving at his workshop for repairs everyday. Based on industry data, he estimates that 40% of the arrivals will agree to have the work repaired at his workshop. His average daily cost at the workshop is $1200. He expects to make a revenue of $200 for each car that is repaired. Johnson would like to know the following information:A) The probability that no car will arrive at his workshop for repair on a given day. B) The probability that he will have at least 4 cars to repair on a given day. C) The expected daily profit assuming that he is able to repair all the arriving cars in a day. D) Develop a probability distribution for this problem.
Answer:
a=0.000000002
b=0.95762
c=$2800
Step-by-step explanation:
Kindly check attached picture for other calculation and the Poisson Probability Distribution for the problem.
What is the slope of the line described by the equation below?
y= 10x + 2
A. -10
B. 10
C. 2
O D. -2
Answer:
B because when you compare y= mx+ c where M is the slope or gradient
Which of the following are valid names for the given triangle? Check all that
apply
T
A
A. ATAY
B. AMAY
C. AMAX
D. AAXM
Ε. ΔΧΜΑ
F. AXMT
Answer:
I think it's just E.
Step-by-step explanation:
When you name triangles, you would often put a Δ and then the letters of the 3 angles. The only answer that fits that criteria is E.
The valid name for the given triangle is ΔΧΜΑ.
What is a triangle?
A triangle is a 3-sided polygon that consists of three edges and 3 vertices. The most vital asset of a triangle is that the sum of the inner angles of a triangle is identical to a hundred and eighty tiers. This belonging is called the attitude sum property of the triangle.
What are the types of triangles?
equilateral, isosceles, scalene, right triangles.
Learn more about triangle here https://brainly.com/question/2938476
#SPJ2
Twice a number is decreased by 7, and this quantity is multiplied by 3. the result is 9 less than 10 times the number. What is the number?
Answer:
(7-2x)3 =9-10x
x= -3
Step-by-step explanation:
we let the number to be x.
twice a number=2x is decreased by 7 that is to say 7-2x, is multiplied by 3, we have (7-2x)3.
the result is 9 less than 10times the number which is =9-10x.
so bringing all these together we have;
(7-2x)3=9-10x.
what is the number?
solving, we have:
(7-2x)3=9-10x
21-6x=9-10x
21-9= -10x+6x
12= -4x
dividing both sides by -4 we have our number
x= -3.
for proof we can substitute x=-3 into the equation.
21-6(-3) =9-10(-3)
21+18=9+30
39=39
The average of four numbers is 38, and the average of the first two numbers is 42, and the average of the last three numbers is 36. What is the second number?
Answer:
40
Step-by-step explanation:
let the numbers be a+b+c+d.
the average of 4 numbers is 38
; (a+b+c+d)/4 = 38
(a+b+c+d) = 152 ......equ1
the average of the first two numbers is 42
; (a+b)/2 = 42
(a+b) = 84 ...... equ2
the average of the last three numbers is 36
; (b+c+d)/3 = 36
(b+c+d) = 108 .....equ3
substitute equ3 into equ1
a + 108 = 152
a= 152 - 108
a = 44
input the value of a into equ2
44 + b = 84
b = 40
the second number is 40.
I hope this helps.
A population has a standard deviation of 5.5. What is the standard error of the sampling distribution if the sample size is 81?
Answer:
[tex]\sigma = 5.5[/tex]
And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:
[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
And the standard error would be:
[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]
And replacing we got:
[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]
Step-by-step explanation:
For this case we know the population deviation given by:
[tex]\sigma = 5.5[/tex]
And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:
[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
And the standard error would be:
[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]
And replacing we got:
[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]
Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):Brand A: 34.36 31.26 37.36 28.52 33.14 32.74 34.34 34.33 34.95Brand B: 41.08 38.22 39.59 38.82 36.24 37.73 35.03 39.22 34.13 34.33 34.98 29.64 40.60 Let formula415.mml represent the population mean for Brand B and let formula417.mml represent the population mean for Brand A.Find a 98% confidence interval for the difference formula419.mml. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.
Answer:
Step-by-step explanation:
For brand A,
Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44
standard deviation, s1 = √(summation(x - mean)²/n
Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338
Standard deviation = √(49.6338/9
s1 = 2.35
For brand B,
Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89
Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024
Standard deviation = √(124.5024/13
s2 = 3.09
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.
Degree of freedom =
(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20
z = 2.528
x1 - x2 = 33.44 - 36.89 = - 3.45
Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935
The 98% confidence interval is
- 3.45 ± 2.935
