Question:
Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283.
a) We will address the question of whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. State hypotheses in terms of two means.
b. Calculate the sample statistic xM - xE
c. Calculate a t-test statistic, using the given estimate of SE.
d. What are the correct (conservative) degrees of freedom for a t-distribution for this test?
e. Use t-distribution methods to find the p-value and draw a rough curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A.
f. State the conclusion of the test in context, using nontechnical language.
Answer:
See explanation below
Step-by-step explanation:
a) The null and alternative hypotheses are:
H0 : uM - uE = 0
H1 : uM - uE > 0
b) Calculating the sample statistic,
xM-xE, we have:
Given xM = 12.70 days
xE = 11.60 days
xM - xE = 12.70 - 11.60 = 1.10 days
Therefore sample statistic = 1.10
c) Calculating the test statistic, using the given estimate of SE, we have:
Given standard error, SE = 0.283
[tex] \frac{xM - xE}{SE} = \frac{12.70 - 11.60}{0.283} = 3.89 [/tex]
Therefore, t test = 3.89
d) The correct degrees of freedom.
We have:
[tex]Min(n_M-1, n_E-1 ) = Min(344-1, 512-1) = Min(343, 511)[/tex]
df = 343
e) p-value:
Pvalue = P(Z > 3.89) = 0.00000602
Since p value is less than significance level of 0.05, we reject null hypothesis H0.
f) Conclusion:
There is enough evidence to conclude that foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins.
Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...
If necessary, round to the hundredths place. (2 places after the decimal)
Answer:
243.01.
Step-by-step explanation:
The first term (a) = 324.
The common ratio (r) = -108/324 = -1/3.
So sum of 9 terms is:
S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)
= 324 ( 1 - (-0.00005076)) / 4/3
= 324 * 1.00005076 / 1.33333
= 243.012.
What is the volume of a hemisphere with a diameter of 51.8 inches round to the nearest 10th of a cubic inch
Answer:
36,388.0 in³
Step-by-step explanation:
The volume of a sphere is usually expressed in terms of the radius as ...
V = (4/3)πr³
Here, we want the volume of 1/2 of a sphere, given the diameter. So, our volume will be ...
V = (1/2)(4/3)π(d/2)³ = (π/12)d³
For the given diameter, the hemisphere volume is ...
V = (π/12)(51.8 in)³ ≈ 36,388.0 in³
Solve for and in the following simultaneous equations below; 5x−4y=8 and 2x+y=11.
Answer:
x=4 and y=3
Step-by-step explanation:
put one of the equations in slope form and solve
Answer:x=4 y=3
Step-by-step explanation:
5x-4y=8.............(1)
2x+y=11................(11)
From (11) y=11-2x
Substitute y=11-2x in 5x-4y=8
5x-4y=8
5x-4(11-2x)=8
Open bracket
5x-44+8x=8
Collect like terms
5x+8x=8+44
13x=52
Divide both sides by 13
13x/13=52/13
x=4
Substitute x=4 in 2x+y=11
2(4)+y=11
8+y=11
Collect like terms
y=11-8
y=3
The sum of the first 7 terms of an arithmetic
sequence 2.5, 7.5, 12.5, 17.5, ... would be:
Answer:
just google it i am not able to put the link to a website which ahs the answer to this sorry :(
Step-by-step explanation:
Answer:
2.5 7.5 12.5 17.5 22.5 27.5 32.5
Step-by-step explanation:
Just add 5 to the previous sum considering it is arithmetic sequence is always addition.
32. Mr. Fernández packed 31 red apples and 41 green apples into a box for a customer. He
packed 8 boxes like this. Mr. Fernández used this equation to find x, the number of apples
he packed into all the boxes.
x = (31 + 41)8
How many apples did Mr. Fernández pack into the boxes?
A. 576
B. 568
C. 80
D. 10,168
HELP!! What are the values of a and b?
The average mark of c
andidates in an aptitude test was 128.5 with a standard deviation of
8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the
extracted scores that are extreme values (outliers)?
Answer:
The average of the extracted scores that are extreme values (outliers) = 102
Step-by-step explanation:
With the logical assumption that the population size is large enough, for a normal distribution,
68% of the data lies within 1 standard deviation of the mean.
95% of the data lies between 2 standard deviations of the mean.
99.7% of the data lies within 3 standard deviations of the mean.
So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.
The mean = 128.5
Standard deviation = 8.2
The range of scores within 3 standard deviations of the mean is obtainable thus
(Mean ± 3standard deviations)
3 × standard deviations = 3 × 8.2 = 24.6
(128.5 ± 24.6) = (103.9, 153.1)
The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.
Hence, the average of the extracted scores that are extreme values (outliers) = 102
Hope this Helps!!!
A bike tire has a diameter of 16 inches What is the radius of the bike What is the circumference of the bike
Please help ASAP! giving BRAINLIEST if correct! What is the factorization of the polynomial below?
Answer:
2(x+6)(x+6)
Step-by-step explanation:
splitting the middle term:
2x²+12x+12x+72
then2x(x+6)+12(x+6)
=(2x+12)(x+6)
=2(x+6)(x+6)(by takin common factor out)
plzz mark me brainliest
Suppose two variables are positively correlated. Does the response variable increase or decrease as the explanatory variable increases? The response variable will increase as the explanatory variable increases. The response variable will decrease as the explanatory variable increases. We can not say whether the response variable will increase or decrease. The response variable will remain constant as the explanatory variable increases. Need Help?
Answer:
Option A
Step-by-step explanation:
Positive correlation describes a relationship between two variables where both variables move in the same direction. In this case, the response variable will increase as the explanatory variable increases.
A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food rewards were equal in appeal. Thus, a pilot study was designed in which participants were asked which of the rewards they preferred. The observed frequencies are as follows:
Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.
1. The appropriate statistical test for this problem is (be specific): ________.
2. What are the expected frequencies for this question?
3. What is the cutoff on the comparison distribution (step 3)?
4. What is the correct calculation for chi-square (step 4)?
Answer:
Step-by-step explanation:
Hello!
A pilot study was conducted to test if three food rewards are equally appealing to the participants.
Of 60 participants surveyed:
16 preferred cupcakes (CC)
26 preferred candy bars (CB)
18 preferred dried apricots (DA)
If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3
1.
The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.
For this example the statistical hypotheses are:
H₀: P(CC)=P(CB)=P(DA)= 1/3
H₁: At least one of the proportions isn't equal to the others.
2.
To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.
[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]
[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]
[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]
3.
The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:
Assuming α: 0.05
[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]
The rejection region is then X²₂ ≥ 7.378
4.
[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]
I hope this helps!
I do not understand how to do this?
Answer:
-8,-7
Step-by-step explanation:
I think
Answer:
try pressing the help button, it looks like it mightve glitched
Step-by-step explanation:
Find the volume of the cylinder. Round your answer to the nearest tenth.
Please help!
Answer:1236.4 ft^3
Step-by-step explanation:
height=h=7ft
Diameter=15ft
Radius=r=15/2=7.5ft
Volume of cylinder=π x r^2 x h
Volume of cylinder=3.14 x (7.5)^2 x 7
Volume of cylinder=3.14x7.5x7.5x7
Volume of cylinder=1236.375
Volume of cylinder=1236.4 ft^3
NEED HELP GEOMETRY ASAP
1. What is the circumference, in inches, of the circular base of the conical hat? Round to the nearest tenth.
2. You want to cover the top of the hat with fabric. What is the surface area, in square inches, that you will cover? (Do not include the base of the cone) Round to the nearest square inch.
Answer:
1. The circumference of the circular base of the conical hat is 52.36 inches
2. The surface area of the cone that needs to be covered is 262 in.²
Step-by-step explanation:
Here we have that the given parameters are;
Diameter, D of circular = 20 in. = 2 × radius R, of the circle
R = 10 in.
Cut out section of cut out sector of circle = 60°
Therefore, circumference of the circular base = π×D×(360 - 60)/360 which gives;
The circumference of the circular base of the conical hat = π×20×(30)/36 = π·50/3 = 52.36 in.
Therefore, the radius of the formed cone = π·50/3/(2·π) = 25/3 = [tex]8\tfrac{1}{3}[/tex] = 8.33 in.
The formed cone satisfies the equation;
R² = h² + r²
Where:
h = Height of the cone
r = radius of the cone
∴ 10² = h² + 8.33²
∴ h² = 10² - 8.33² = 30.56 in.
The lateral surface area of the cone = π×r×l where l = R, we therefore have;
The lateral surface area of the cone = π×8.33×10 = [tex]\pi \cdot 8\tfrac{1}{3}[/tex] = 261.8 in.² = 262 in.².
The surface area of the cone that needs to be covered = The lateral surface area of the cone = 262 in.².
if a sample of 57 swimmers is taken from a population of 135 swimmers, the population mean is the mean of how many swimmers' times?
Answer:
135
Step-by-step explanation:
A P E X
If you put all the sunflowers together end to end, what would be the total length of all the sunflowers?
Answer:
7 1\68
Step-by-step explanation:
all i did was look up a fraction calculator
calculator soup is the one i used :)
Consider the graph of the exponential function, y =3(2)^x. The x- intercept of the graph is
Answer:
the x intercept is 2
Step-by-step explanation:
I just went over this unit
Answer:
2
Step-by-step explanation:
Figure 4 shows a container in the shape of an inverted right circular cone which contains some water.
The cone has an internal radius of 2.5 m and a vertical height of 4 m.
At time t seconds, the height of the water is h m, the volume of the water is V m3 and water is modelled as leaking from a hole in the bottom of the container at a rate of h m3 s –1.
see on picture!
Given that the container was initially full of water,
(b) find an equation, in terms of h and t, to model this situation.
(3)
It takes close to 43 minutes for the container to empty.
(c) Use this information to comment on the suitability of this model.
Answer: a) See below; b) 2/5([tex]h^{\frac{5}{2} }[/tex]) = - [tex]\frac{1}{200}[/tex].t + 0.215
Step-by-step explanation:
a) To determine the radius (x) of the volume of water remaining, use proportionality of similar triangles:
[tex]\frac{x}{2.5} = \frac{h}{4}[/tex]
x = 0.625h
Volume is
V = 1/3.π.(0.625h)².h
V = 1/3.π.0.391.h³
Using the chain rule to determine the rate of change of height in function of t:
[tex]\frac{dV}{dt} = \frac{dV}{dh} . \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dV}{dt}/\frac{dV}{dh}[/tex]
[tex]\frac{dh}{dt} =[/tex] (π/512).[tex]\sqrt{h}[/tex] / 0.391.π.h²
[tex]\frac{dh}{dt} =[/tex] (π . [tex]\sqrt{h}[/tex]) / 512.0.391.π.h²
[tex]\frac{dh}{dt} =[/tex] [tex]\frac{h^{\frac{-3}{2} } }{200}[/tex]
[tex]h^{\frac{3}{2} }\frac{dh}{dt}=\frac{-1}{200}[/tex]
b) To find an equation:
[tex]h^{\frac{3}{2} }[/tex] dh = -(1/200) dt
∫ [tex]h^{\frac{3}{2} }[/tex] dh = -1/200 ∫dt
[tex]\frac{2.h^{\frac{5}{2} } }{5}[/tex] = [tex]\frac{-1.t}{200}[/tex] + c
It is known that it takes 43 minutes to empty the cone, so:
0 = [tex]\frac{-1.43}{200}[/tex] + c
c = 0.215
The equation is:
[tex]\frac{2.\sqrt[5]{h^{2}} }{5}[/tex] = [tex]\frac{-t}{200}[/tex] + 0.215
c) The equation shows how height and time are inversely proportional to each other: as time goes up, height goes down. Mathematically, though, time cannot be negative. So, the model is suitable for modeling time and height but is not mathematically correct.
Consider this quadratic equation
X^2+2x+7=21
Answer:
x = sqrt(15) - 1 or x = -1 - sqrt(15)
Step-by-step explanation:
Solve for x:
x^2 + 2 x + 7 = 21
Subtract 7 from both sides:
x^2 + 2 x = 14
Add 1 to both sides:
x^2 + 2 x + 1 = 15
Write the left hand side as a square:
(x + 1)^2 = 15
Take the square root of both sides:
x + 1 = sqrt(15) or x + 1 = -sqrt(15)
Subtract 1 from both sides:
x = sqrt(15) - 1 or x + 1 = -sqrt(15)
Subtract 1 from both sides:
Answer: x = sqrt(15) - 1 or x = -1 - sqrt(15)
The ratio of boys to girls at King Middle School is 3:2. What is the ratio of girls to all
students?
3:5
2:5
2:3
3:2
Answer:
2:5
Step-by-step explanation:
your welcome. jsvsjgbdjshwbkshd
Answer:
The answer will be 2:5 Ratio.
Step-by-step explanation:
The explanation for this answer is going to be adding 3 + 2 Ratio = 5.
Once we have 5 we put the 5 on the right Which means all then we put the Girls (2) on the left. Hope you found this answer helpfull.
In general, how is the graph of g(x) = | [tex]x - h[/tex] | + [tex]k[/tex] related to the graph of f(x) = | x |? GIVING BRAINLIEST!!
Answer:
The graph of g(x) = |x - h| + k is a translation of h units horizontally and k units vertically of the graph of f(x) = | x |.
Hope this helps.
Answer:
H units horizontally, k units vertically
Step-by-step explanation:
What is the median of the following numbers?
1, 2, 10, 6, 4, 4, 6, 3, 1,4
Answer:
4
Step-by-step explanation:
The median is the middle number after ordered into numberical order. If there's two and the numbers are different, you add them and divide the total by 2.
Answer: 4
Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.
So let's write our data set from least to greatest.
So we have 1, 1, 2, 3, 4, 4, 4, 6, 6, 10.
Now, notice that there are two numbers that appear in the middle.
I have underlined them above.
When two numbers appear in the middle that are the same number (4 and 4), the median will be the same number too.
So the median of the given data set is 4.
A 25 lb. bag Balkfoods Small Red Beans cost $52.92. What is the unit price
per Ib?
Answer:
$2.1 per pound
Step-by-step explanation:
price/pounds
52.92 / 25 = 2.1
could you help me with this question? it is attached in an image
Answer:
its either 1 or 4 i think
A bottle of has a capacity of 0.43 L. How many milliliters of shampoo does the bottle contain (1 L = 1000 mL
Answer:
1 = 1000
0.43 L = _________ mL
0.43 * 1000 = 430 mL
430 mL is the answer.
Hope this helps
What is the answers?
Answer:
[tex]\frac{(x + 1)}{(x + 3)}[/tex]
Step-by-step explanation:
If you ignore the 7x for the moment, you can see that the numerator can be factored into (x-5)(x+1), and the denominator can factored into (x-5)(x+3).
The (x+5)s can cancel out, so you are left with [tex]\frac{(x+1)}{(x+3)}[/tex] times [tex]\frac{7x}{7x}[/tex]. Since 7x/7x is just equal to 1, our final answer is (x+1)/(x+3).
Hope this helped! :)
Find the surface area of the polyhedron below. The area of each base is 65 cm^2
Answer:
D. 290 square cm
Step-by-step explanation:
Surface area of polyhedron
[tex]= 2 \times 65 + 7 \times 8 + 4 \times 8 + 3 \times 8 + 3(2 \times 8) \\ = 130 + 56 + 32 + 24 + 48 \\ = 290 \: {cm}^{2} [/tex]
40/50 to a simpel fraction
Answer:
4/5
Step-by-step explanation:
just divide by 10 since that's the largest number that both numbers can equally be divisible by
Answer:
4/5 because 40/50 simplified is 4/5 bc you knock off the zeros for question like that
Step-by-step explanation:
Tyler simplified the expression x Superscript negative 3 Baseline y Superscript negative 9. His procedure is shown below.
x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction
What is Tyler’s error?
Answer:
[tex]y^{-9}\neq \dfrac{1}{y^{-9}}[/tex]
Step-by-step explanation:
Tyler simplified the expression: [tex]x^{-3}y^{-9}[/tex] as shown below:
[tex]x^{-3}y^{-9}=\dfrac{1}{x^3}X \dfrac{1}{y^{-9}}=\dfrac{1}{x^3y^{-9}}[/tex]
We notice that in Tyler's work:
[tex]y^{-9}= \dfrac{1}{y^{-9}}[/tex]
Whereas, the correct form would have been:
[tex]y^{-9}= \dfrac{1}{y^{9}}[/tex]
Making our solution:
[tex]x^{-3}y^{-9}=\dfrac{1}{x^3}X \dfrac{1}{y^{9}}=\dfrac{1}{x^3y^{9}}[/tex]
What is the slope of a line perpendicular to a line with slope -8
Answer:
1/8
Step-by-step explanation:
You would need to get the reciprocal of negative eight and then change the sign so you would get 1/8
