Answer:
Colin can do this is 272 ways.
Step-by-step explanation:
The first counter goes to Obi and the second to Zeema, so the order is important. This means that we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Two counters from a set of 17. So
[tex]P_{(17,2)} = \frac{17!}{(17-2)!} = 272[/tex]
Colin can do this is 272 ways.
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2
SOMEBODY HELP
Jill bought 7 books more than Sam. If Sam and Jill together have 25 books, find the
number of books Sam has.
Answer:
Jill bought 16 books and Sam bought 9 books
Step-by-step explanation:
Let the number of books that Jill bought be j.
Let the number of books that Sam bought be s.
Jill bought 7 more books than Sam:
j = 7 + s
They bought 25 books altogether:
j + s = 25
Put j = 7 + s into the second equation:
7 + s + s = 25
7 + 2s = 25
2s = 25 - 7 = 18
s = 18/2 = 9 books
Therefore:
j = 7 + s = 7 + 9
s = 16 books
Jill bought 16 books and Sam bought 9 books.
the linear equation y=2x represents the cost y of x pounds of pears. which order pair lies on the graph of the equation? A. (2,4) B. (1,0) C.(10,5) D. (4,12)
Answer:
A. (2, 4)
Step-by-step explanation:
The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...
(x, 2x)
That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).
It is the case that you have (x, 2x) for (2, 4).
The point (2, 4) lies on the graph of y = 2x.
I NEED HELP ASAP PLEASE! :)
Answer:
option 1
Step-by-step explanation:
[tex]r=\sqrt{(5\sqrt{2})^{2}+(-5\sqrt{2})^{2} } \\\\=\sqrt{25*2+25*2}\\\\ =\sqrt{50+50}\\\\=\sqrt{100}\\\\=10[/tex]
[tex]x=tan^{-1}(\frac{-5\sqrt{2}}{5\sqrt{2}})\\\\x=tan^{-1} (-1)\\x=\frac{7\pi}{4}[/tex]
[tex]re^{ix}=10e^{i\frac{7\pi}{4}}[/tex]
Charles's law states that at constant pressure, the volume of a fixed amount of gas varies directly with its temperature measured in Kelvins. A gas has a volume of 250 ml at 300°K. a.) Write an equation for the relationship between volume and temperature. b.) What is the volume if the temperature increases at 420°K?
Answer:
equation is pv=nRT
p, n, R are constants
so, v is directly proportional to Temperature
v1/v2=T1/T2
250/v2=300/420
v2=350
A pair of surfers collected data on the self-reported numbers of days surfed in a month for 30 longboard surfers and 30 shortboard surfers. Complete parts a and b below.
Longboard: 2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Shortboard: 17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
a) Compare the typical number of days surfing for these two groups.
The median for the longboards was________ days, and the median for the shortboards was_______ days, showing that those with________ typically surfed more days in this month
b) Compare the interquartile ranges.
The interquartile range for the longboards was________ days, and the interquartile range for the shortboards was_______ days, showing more variation in the days surfed this month for the________
Answer:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Step-by-step explanation:
Longboard:
2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Sorting in ascending order, we have:
[tex]2, 3, 5, 6, 7, 7, \boxed{8, 8}, 9, 10, 10, 11, 11, 12, \boxed{13, 14,} 15,15, 16, 16, 16, 17, \boxed{18, 18}, 19, 20, 21, 22, 24 , 24[/tex]
Median [tex]=\dfrac{13+14}{2}=13.5[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{18+18}{2}=18\\$Interquartile range, Q_3-Q_1=18-8=10[/tex]
Shortboard
17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
Sorting in ascending order, we have:
[tex]5, 6, 6, 7, 7, 7, \boxed{8, 8,} 8, 10, 10, 10, 12, 12, \boxed{13, 13} 14, 15, 16, 16, 16, 16, \boxed{17, 20,} 22, 23, 23, 24, 24, 25[/tex]
Median [tex]=\dfrac{13+13}{2}=13[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{17+20}{2}=18.5\\$Interquartile range, Q_3-Q_1=18.5-8=10.5[/tex]
Therefore:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Please answer this correctly
Answer:
75%
Step-by-step explanation:
The numbers that are not 5 are 6, 7, and 8.
3 numbers are not 5 out of 4 total numbers on the spinner.
3/4 = 0.75
= 75%
Answer:
75%
Step-by-step explanation:
Total no.s = 4
Divided in parts = 25%
P(not 5) = 75%
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. c) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144d) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
Answer:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Step-by-step explanation:
Confidence interval:
Confidence level of x%
We build from a sample.
Between a and b.
Intepretation: We are x% sure that the population mean is between a and b.
In this question:
90%
45 CEO's
Between ($139,048, $154,144).
So
We are 90% sure that the mean salary of all CEO's falls within this interval.
The correct answer is:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Let f(x)= |x| and g(x) = x+2. What are the domain and range of (fog)(x)?
If [tex]f(x)=\mid x\mid[/tex] and [tex]g(x)=x+2[/tex] then [tex]f(g(x))=\mid x+2\mid[/tex].
The domain is [tex]x\in(-\infty, +\infty)=\mathbb{R}[/tex].
The range is [tex]y\in[2,+\infty)[/tex].
Hope this helps.
Answer:
D) domain: all real numbersrange: y>0Step-by-step explanation:
with range there is a horizontal line under the > sign, just as a side note:D
BRANLIEST?
Choose the name of this figure.
A.
line
B.
angle
c.
line segment
D.
ray
Answer:
we dont see aa figure
Step-by-step explanation:
Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answer:
4 and 4
Step-by-step explanation:
We have 2 numbers that will be X and Y
X * Y = 16 => Y = 16 / X
We must minimize the sum, therefore:
S = X + Y
S = X + 16 / X
we derive and equal 0 and we are left with:
dS / dA = 1 - 16 / (X ^ 2) = 0
1 = 16 / X ^ 2
X ^ 2 = 16
X = 4
in the case of Y:
Y = 16/4 = 4
Therefore the numbers are 4 and 4.
The two positive numbers are 4 and 4
Let the two numbers be x and y
If the product of both numbers is 16, hence;
xy = 16 ........................... 1
If the sum will be at the minimum, hence x + y = minimum
From equation1, x = 16/ y
Substitute into the second equation to have;
16/y + y = A(y)
A(y) = 16/y + y
For the expression to be at a minimum, hence dA/dy = 0
dA/dy = -16/y² + 1
0 = -16/y² + 1
0 - 1 = -16/y²
-y² = -16
y = √16
y = 4
Recall that xy = 16
4x= 16
x = 4
Hence the two positive numbers are 4 and 4
LEarn more here: https://brainly.com/question/13598452
Which functions have an axis of symmetry of x = -2? Check all that apply. A. f(x) = x^2 + 4x + 3 B. f(x) = x^2 - 4x - 5 C. f(x) = x^2 + 6x + 2 D. f(x) = -2x^2 - 8x + 1 E. f(x) = -2x^2 + 8x - 2
Answer:
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Step-by-step explanation:
The axis of symmetry is found by h = -b/2a where ax^2 +bx +c
A. f(x) = x^2 + 4x + 3
h = -4/2*1 = -2 x=-2
B. f(x) = x^2 - 4x - 5
h = - -4/2*1 = 4/2 =2 x=2 not -2
C. f(x) = x^2 + 6x + 2
h = -6/2*1 = -3/2 = x=-3/2 not -2
D. f(x) = -2x^2 - 8x + 1
h = - -8/2*-2 = 8/-4 =-2 x=-2
E. f(x) = -2x^2 + 8x - 2
h = - 8/2*-2 = -8/-4 =2 x=2 not -2
Answer:
Hey there! The answer to this question is
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
PLEASE HELP ME! Simplify the expression 3 4 (1440) + 295.25 + (-33.50) to determine how much money the theater brought in.
Answer:
1341.75
Step-by-step explanation:
I did the math :)
The guy above me is correct
Write the Maclaurin series for f(x) = x^7e^x5. (2 points) a) the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial b) the summation from n equals 0 to infinity of the quotient of x to the 12th power and the quantity n plus 5 factorial c) the summation from n equals 0 to infinity of the quotient of x to the quantity 5 times n plus 7 power and n factorial d) the product of x raised to the 5 times n power and the summation from n equals 1 to infinity of the quotient of x to the 7th power and n factorial
Recall that
[tex]e^x=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]
Then
[tex]e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n}}{n!}[/tex]
and
[tex]x^7e^{x^5}=\displaystyle\sum_{n=0}^\infty\frac{x^{5n+7}}{n!}[/tex]
what expression is equivalent to 6+(-x)+2x(-7)+2x
Answer:
I hope this will help you :)
Step-by-step explanation:
6+(-x)+2x(-7)+2x
6-x+2x✖️(-7)+2x
6-x-14+2x
6-14-x+2x
-8+x
Which of the following indicates the subtraction property of equality when solving the equation 86 – 2 (9x + 4) = 12x + 18 A) 2(9x + 4) = 86 – 12x – 18 B) x = 2 C) –2(9x + 4) = 12x + 18 – 86 D) 86 – 18x – 8 = 12x + 18
Answer:
D) 86 – 18x – 8 = 12x + 18
X = 2
Step-by-step explanation:
86 – 2 (9x + 4) = 12x + 18
This question has a straight forward answer...
It's just to open up the bracket and ensure that the negative sign before the bracket multiply the values in the bracket exactly.
So opening up the bracket gives us this as the answer
86 - 18x -8 = 12x +18
86-18-8 = 12x+ 18x
60 = 30x
X = 2
a water storage tank is in the shape of a hemisphere. If the radius is 29ft, approximate the volume of the tank in cubic feet
Answer:
The answer is 51080.2 cubic feetStep-by-step explanation:
Volume of a hemisphere is given by
[tex]V = \frac{2}{3} \pi {r}^{3} [/tex]
where r is the radius of the hemisphere
From the question
r = 29 ft
Substitute the value of r into the formula
That's
[tex]V = \frac{2}{3} \pi \times {29}^{3} [/tex]
[tex]V = \frac{48778}{3} \pi[/tex]
We have the final answer as
V = 51080.2 cubic feetHope this helps you
The rectangle has an area of 60 square feet. Find its dimensions (in ft). (x + 4) feet smaller value ___________________ ft larger value ____________________ ft
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.
smaller value ___________________ ft
larger value ____________________ ft
Answer:
Smaller value = 6 ft
Larger value = 10 ft
Step-by-step explanation:
Recall that the area of a rectangle is given by
[tex]Area = W \times L[/tex]
Where W is the width and L is the length of the rectangle.
It is given that the rectangle has an area of 60 square feet.
[tex]Area = 60 \: ft^2 \\\\60 = W \times L \\\\[/tex]
It is also given that the length of the rectangle is 4 ft more than its width
[tex]L = W + 4[/tex]
Substitute [tex]L = W + 4[/tex] into the above equation
[tex]60 = W \times (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\[/tex]
So we are left with a quadratic equation.
We may solve the quadratic equation using the factorization method
[tex]W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\[/tex]
So,
[tex](W + 10) = 0 \\\\W = -10 \\\\[/tex]
Since width cannot be negative, discard the negative value of W
[tex](W - 6) = 0 \\\\W = 6 \: ft \\\\[/tex]
The length of the rectangle is
[tex]L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\[/tex]
Therefore, the dimensions of the rectangle are
Smaller value = 6 ft
Larger value = 10 ft
Verification:
[tex]Area = W \times L \\\\Area = 6 \times 10 \\\\Area = 60 \: ft^2 \\\\[/tex]
Hence verified.
Please answer this correctly without making mistakes
Answer: Anything above 2
Step-by-step explanation:
Answer: 3,4,5,6,7,8,9 (Any of these digits work)
Step-by-step explanation:
We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.
3318.7≥3260.2
Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.
Pls hurry least to greatest
Answer:
First choice
Step-by-step explanation:
Start by arranging the exponents of 10 in ascending order.
9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7 * 10^3
The exponents are in ascending order, -8, -6, 3, 3
Since the last two exponents are equal, we must compare the numbers that multiply the powers of 10. They are 2.5 and 7. Since 2.5 < 7, ascending order is 2.5, 7. That means the line above is in ascending order.
Answer: First choice
a)3x-1/5=2x+3/7
b)4x/5-3x/10=2
is this what u need.....
1/3 times the difference of a number and five is -2/3 which equation best shows this
Answer:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Step-by-step explanation:
Let the number be x
Difference of a number & 5 : x-5
1/3 time the difference of a number & 5: 1/3 (x-5)
Equation:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Solution:
[tex]x-5=\frac{-2}{3}*\frac{3}{1}\\\\x-5=-2\\\\x=-2+5\\x=3[/tex]
Please answer this correctly
Answer:
8/25
Step-by-step explanation:
The probability of picking a number less than 9 is 4/5.
The probability of picking an even number is 2/5.
[tex]4/5 \times 2/5[/tex]
[tex]=8/25[/tex]
If sin t=0.29 and sin w = 0.43, both t and w are positive, and the angles determined by t and w are in quadrant 2, then which of the following statements is true? Explain your selection
a. t>w
b. w>t
c. cannot be determined
Answer:
a. t>w
Step-by-step explanation:
Sin t= 0.29
t = sin^-1(0.29)
t= 16.86°
Sin w= 0.43
W = sin^-1(0.43)
W= 25.47°
Angles in the second quadrant are positive in sine and they are generally determined by subtracting the initial value from 180°
For t= 180°-16.86°
t = 163.14°
For w = 180°-25.47°
W= 154.53°
163.14°>154.53°
t>w
Please answer this correctly without making mistakes
Answer:
A digit that makes this sentence true is 4.
Step-by-step explanation:
Since the first digit in the number to the left is 3, you simply have to find a digit greater than 3. Here are the possibilities:
4
5
6
7
8
and
9
Out of any of these you can choose, I chose 4.
9514 1404 393
Answer:
3, or any greater digit
Step-by-step explanation:
Suppose the digit is 'd'. Then the value on the right is ...
69.436 +100d
Subtracting the value on the left, we want the difference greater than 0.
69.436 +100d - 352.934 > 0
100d -293.498 > 0 . . . . simplify
100d > 293.498 . . . . . . . add 293.498
d > 2.93498 . . . . . . . . . . divide by 100
That is d is any single digit greater than 2.9. Those digits are ...
d ∈ {3, 4, 5, 6, 7, 8, 9}
Any digit 3 or greater makes the sentence true.
Solve the equation. Round the solution to the nearest tenth . Enter the solution set of the equation . 2P o =P 0 (1.053)^ t
Answer: t= 13.4
Step-by-step explanation:
The given equation is [tex]2P_0=P_0(1.053)^t[/tex]
To solve this equation for 't', we first divide both sides by [tex]P_0[/tex], we get
[tex]2=(1.053)^t[/tex]
Taking log on both the sides, we get
[tex]\log 2= \log(1.053)^t[/tex]
Since [tex]\log a^b=b\log a[/tex]
Then,
[tex]\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=\dfrac{0.30103}{0.02243}\\\\\Rightarrow t=13.4208649131\approx13.4[/tex]
Hence, the value of t is 13.4.
In a jar of coins, 18 out of the 40 coins are dimes. Express the fraction of the coins
that are dimes in three different ways below: (a) as a fraction, (b) as a decimal, and (c) as a percent.
Use long division to determine the decimal.
(a) as a fraction
(b) as a decimal
(c) as a percent
Answer:
Percent: 20%
Fraction: 1/5
Decimal: 0.20
Step-by-step explanation:
8:40*100 =
( 8*100):40 =
800:40 = 20%
Percent to fraction:
20%=20/100
= 0.2
=0.2×10/10
=2/10
=1/5
Percent to decimal:
20/100 = 0.20
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?
Answer:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Step-by-step explanation:
Given:
There are two types of boxes i.e. Large and Small
Let the weight of Large boxes = L kg
Let the weight of Small boxes = S kg
As per given statement:
A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.Writing equation for above:
[tex]8L + 4S = 201[/tex] ....... (1)
A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.Writing equation for above:
[tex]3L + 2S = 82 ....... (2)[/tex]
Now, by solving the equations (1) and (2), we can get the values of L and S.
Multiplying equation (2) with 2 and subtracting from equation (1):
[tex]8L + 4S = 201[/tex]
-
[tex]2 \times (3L + 2S) = 82 \times 2[/tex]
[tex]8L + 4S = 201[/tex]
-
[tex]6L + 4S = 164[/tex]
--------------------
[tex]2L = 37[/tex]
L = 18.5 Kg
Putting value of L in equation (1):
[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]
So, the answer is:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Population divided into groups. Some members of each group are surveyed. This is stratified sampling
Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.