When the variances are known and the sample size is high, a z-test is used to assess if two population means vary. The mean of the two players is not the same.
What is a Z-test?When the variances are known and the sample size is high, a z-test is used to assess if two population means vary.
In order to execute an appropriate z-test, the test statistic is expected to have a normal distribution, and nuisance factors such as standard deviation should be known.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ H_a: \mu_1 & \ne & \mu_2 \end{array}[/tex]
This corresponds to a two-tailed test, and a z-test for two means, with known population standard deviations, will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is [tex]z_c = 1.96[/tex]
The rejection region for this two-tailed test is R={z:∣z∣>1.96}
(3) Test Statistics
The z-statistic is computed as follows:
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
[tex]\begin{array}{ccl} z & = & \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ {\sigma_1^2/n_1} + {\sigma_2^2/n_2} }} \\\\ & = & \displaystyle \frac{ 30.1 - 25.5}{\sqrt{ {9.112^2/70} + {12.602^2/70} }} \\\\ & = & 2.475 \end{array}[/tex]
(4.) The decision about the null hypothesis
Since it is observed that |z| = 2.475 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is p = 0.0133p=0.0133, and since p = 0.0133 < 0.05p=0.0133<0.05, it is concluded that the null hypothesis is rejected.
(5.) As it is concluded that the null hypothesis H₀ is rejected. Therefore, there is enough evidence to claim that the population mean μ1 is different than μ2.
Hence, the mean of the two players is not the same.
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Raheem runs five times a week. His route is 4 1/3 miles long. How many miles does he run each week?
Answer:
21.6666666667
If you have to round it up it is 22.
Step-by-step explanation:
If he runs 5 times a week and his route is 4 1/3 then he runs that five times a week you do 5x4 1/3 and that is how you get your answer
To advance in a computer game, players need to open a door by choosing one number
on each of the dials. What is the probability that
the combination starts with 8?
Answer:
1/3 or 33.3333...%
Step-by-step explanation:
My understanding of this situation is that each dial represents a number in the combination. In order for the combination to start with 8, the first dial needs to land on 8. Since there are three numbers on the dial, the probability that the combination starts with 8 is 1/3. Hope I helped :)
Find the volume will give brainlest
A consumer survey conducted in two consecutive years found that a fixed basket of goods and services cost $36.00 in year 1 and $36.75 in year 2 the inflation rate from year 1 to year 2 is
Answer:
2.08 %
Step-by-step explanation:
(36.75 - 36.00) / 36.00 = .0208 = 2.08 %
50 points each question. Please help. How do I solve?
[tex]\text{Given that,}\\\\~~~1+ \ln (3xy) = e^{3x-y}\\\\\\\implies \dfrac d{dx} \left[1 + \ln (3xy) \right] = \dfrac{d}{dx} \left(e^{3x-y} \right)\\\\\\\implies \dfrac{1}{3xy} \cdot 3 \dfrac{d}{dx}(xy) = e^{3x-y} \cdot \left(3 - \dfrac{dy}{dx} \right)\\ \\\\\implies \dfrac 1{xy} \left( x \dfrac{dy}{dx} + y \right)= e^{3x-y} \cdot \left(3 - \dfrac{dy}{dx} \right)\\\\\\\implies \dfrac 1y \dfrac{dy}{dx} + \dfrac 1x = 3e^{3x-y}- e^{3x -y} \dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac 1y \dfrac{dy}{dx} + e^{3x-y} \dfrac{dy}{dx} = 3e^{3x-y} - \dfrac 1x\\\\\\\implies \left( \dfrac 1y+ e^{3x-y} \right)\dfrac{dy}{dx} = 3e^{3x-y} - \dfrac 1x\\\\\\\implies \dfrac{dy}{dx}=\dfrac{3 e^{3x-y} -\dfrac 1x}{\dfrac 1y+ e^{3x-y} }\\\\\text{At point}~ (x,y) = (1/3, 1), \text{slope of the tangent line,}\\\\m=\dfrac{dy}{dx} = 0\\\\\text{Hence the equation of tangent line,}\\\\~~~y-1 =0\\\\\implies y=1[/tex]
The figure shows the dimensions for a birthday gift. Find the minimum amount of wrapping paper, in square inches, needed to cover the gift. Round your answer to the nearest whole inch.
sqauare inches
The minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.
What is of total surface area of the rectangular prism?The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of prism.
Total surface area of the rectangular prism is calculated with the following formula.
[tex]A=2(lb+bh+lh)[/tex]
Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.
The minimum amount of wrapping paper required to cover the gift is equal to the surface area of the figure.
The figure is made with different sides, The area of all the sides is equal to the surface area of the figure. The surface area of it is,
[tex]A=2(5\times8)+(15\times8)+(15\times10)+2(\dfrac{1}{2}3\times8)+(15\times5)+(15\times11)\\A=614\rm\;in^2[/tex]
Thus, the minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.
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Passengers on many commercial flights may make calls from a telephone provided
by the airline. On a certain airline, a call costs $3 to connect plus $2 for each
minute. Which linear equation best represents c, the total cost for a call that lasts m
minutes?
Answer:
c = 3 + 2m
Step-by-step explanation:
Let c = total cost of call (in dollars)
Let m = number of minutes
Given:
Connection fee = $3Cost per minute = $2⇒ c = 3 + 2m
Does anyone know how to solve this hard question without using a calculator
Answer:
sq rt 2/2
Step-by-step explanation:
Use unit circle to find the answer.
Find the length of the unknown side round your answer to the nearest 10th
Triangle in picture above ☝️
Answer:
72.8
Step-by-step explanation:
How to solve 8x+y=23
-10x-y=-27
Here,
8x + y = 23 - 10x - y = - 27
10(8x + y) = 23 × 10 8 (- 10x - y) = - 27 × 8
80x + 10y = 230 ---> (i) - 80x - 8y = - 216 ----> (ii)
By elimination method,Equation (i) - (ii)(80x + 10y) - (-80x - 8y) = 230 - (-216)
=> 80x + 10y + 80x + 8y = 230 + 216
=> 10y + 8y = 446
=> 18y = 446
=> y = 446/18
=> y = 24.7
Putting the value of "y" in Equation (i)80x + 10y = 230
=> 80x + 10 × 24.7 = 230
=> 80x + 247 = 230
=> 80x = 230 - 247
=> 80x = -17
=> x = -17/80
=> x = - 0.21
Therefore the values of "x" and "y" arex = -0.21 and y = 24.7
Hope it helpsIn the triangle, angle RST is 90°. RS= 4cm and ST=3 cm. What is the length of RT? R 4 cm S T 3 cm
Step-by-step explanation:
RT^2=RS^2+ST^2
RT^2=16+9=25
RT=√25=5
The answer is 5
Which fractions are equivalent to the value of
2
10
+
20
100
? Drag and drop the fractions into the box.
Lets see
2/10+20/1002/10+2/102+2/104/102/5Answer:
thanks just needed points
Step-by-step explanation:
If 3 inches equals 4 feet how much does 4 inches equal
Step-by-step explanation:
so, hypothetically,
3 in = 4 ft
4 in = 4 × 1 in = 4 × 3 in / 3 = 4 × 4 / 3 = 16/3 =
= 5.333333333... ft or 5 1/3 ft
Izzie bought 6 hoodies that
each cost the same amount
and a pair of shorts that
cost $23. The items she
bought cost a total of $194
before tax was added. What
was the cost of each
hoodie? (set up an equation
to solve)
Answer:
$ 28.50
Step-by-step explanation:
6 hoods + 23 = 194
6 hoods = 171
hood = $ 28 . 50
what is 5/12 - 1/3 = in simplest form
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
See picture below for explanation:
Use the Multiplication Law of Exponents to solve the expression below.
6 1/2 . 6 1/2=
The base of 6 is the same, so add 1/2+1/2 =1
6^1 = 6
Answer:
The asnwer is
The base of 6 is the same, so add 1/2+1/2 =1
6^1 = 6
Step-by-step explanation:
I hope i helped you very much
Nevada is almost twice the size of which country?
A. Algeria
B. Mauritania
C. Kenya
D. Democratic republic of the Congo
Please help me
The point (3,6) is represented on the graph. Which point also belongs on this graph?
Line graph. Line starts at (0, 0). One point plotted: (3, 6).
Answer:
Your answer would be (36,72)
Step-by-step explanation:
Justin is on a road trip. Over the past 2 days, he has driven a total distance of 715 miles at an average speed of 65 miles per hour. If
Justin drove 2 hours today, how many hours did he drive yesterday?
Answer:
1 hour did he drive yesterday
Jenna surveyed her friends, asking each of them, "How many times have you been to the aquarium?" The resulting data set has a distribution that can be described several ways.
Select from the drop-down menus to correctly complete the statements about the distribution.
The distribution can be described by its shape. If there are more higher values than lower values, the distribution is skewed
Choose...
.
The distribution can be described by its center. If the distribution is skewed left or right, the
Choose...
is an accurate measure of center.
The distribution can be described by its spread. If the data set does not have an outlier, the
Choose...
is an accurate measure of spread.
In the research, the distribution is described by its shape. If there are more higher values than lower values, the distribution is skewed left.
How to illustrate the research?It should be noted that when the distribution of data is skewed to the left, the mean is less than the median.
The distribution can be described by its center. If the distribution is skewed left or right, the median is an accurate measure of center.
The distribution can be described by its spread. If the data set does not have an outlier, the interquartile range is an accurate measure of spread.
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Answer:
left, median, and range or the IQR
Step-by-step explanation:
What type of triangle can an equilateral be?
isosceles triangle
right triangle
acute triangle
obtuse triangle
Answer:
Acute triangle
Step-by-step explanation:
Logan calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: geography, math, English, and theat geography: MAD of 3.5
math: MAD of 1.36
English: MAD of 1.8
theater, MAD of 3.15
In which class were his scores the closest together?
geography
math
theater
English
Using it's concept, it is found that due to the lowest Mean Absolute Deviation, his scores were closest together in Math.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean. Hence, lower values of the MAD means that the distribution is closer together.Of the four classes, Math was the lower MAD, hence it has the scores that are closest together.
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What is the value of(-4)(-4)(-4)
Answer:
-64
Step-by-step explanation:
-4x-4x-4
A boxplot is also known as a/an
A. side plot
B. box and whisker plot
C. stem and leaf plot
D. stemplot
B. box and whisker plot
A boxplot—sometimes called a box and whisker plot—is a dense display that aims to provide lots of context for any given dataset. The chart visually represents several summary metrics in a single view: minimum: the smallest value maximum: the largest value
If you know the volume of a rectangular prism and the area of the base, how can you find the height?
what is the sum of two numbers is "-7." Two times the first number equals 4 the second number. Find the two numbers.
Answer:
[tex]\sf \text{The numbers are $\dfrac{-14}{3} $ and $\dfrac{-7}{3}$}[/tex]
Step-by-step explanation:
Let the numbers be x , y
Sum of two numers = -7
x + y = -7------------(I)
Two times the first number equals 4 the second number.
2x = 4y ----------(II)
Divide both sides by 2
[tex]\sf \dfrac{2x}{2}=\dfrac{4y}{2}[/tex]
x = 2y
Subtitute x = 2y in equation (I)
2y + y = -7
3y = -7
y = -7/3
Plugin y = -7/3 in equation (II)
[tex]\sf 2x = 4*\dfrac{-7}{3}\\\\2x = \dfrac{-28}{3}\\\\x =\dfrac{-28}{3*2}\\\\x = \dfrac{-14}{3}[/tex]
The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 800 patients, 5% reported headaches.
Construct a 90% confidence interval estimate of the proportion of Lipitor users who will report headaches as a side effect. NO explanation needed or will be reported.
Using the z-distribution, it is found that the 90% confidence interval estimate is given by (0.0373, 0.0627).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The sample size and the estimate are given, respectively, by [tex]n = 800, \pi = 0.05[/tex].
Hence, the bounds of the interval are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0373[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0627[/tex]
The 90% confidence interval estimate is given by (0.0373, 0.0627).
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Selecting a black vehicle with a leather interior
A 12 sided die is rolled find the probability of rolling a two
Answer:
1/12
Step-by-step explanation:
so we know the total you have is a 12 dice cube yes? yes.
there fore you denomanator is the the total of everything-12.
there's only 1 #2 on the 12 sided dice this cause you to get 1/12
Find the value of angle W
Answer:
w = 73°
Step-by-step explanation:
The relations involved in solving this figure are ...
linear pairs are supplementarythe angle sum for the quadrilateral is 360°__
The linear pair at lower left gives us a relation we can solve for x:
x +(3x -24) = 180
4x = 204
x = 51
Then the sum of angles inside the quadrilateral is ...
w +(x +15) +(2x -10) +(3x -24) = 360
w +(51 +15) +(2(51) -10) +(3(51) -24) = 360
w +66 +92 +129 = 360
w = 360 -287 = 73
Angle W is 73°.
_____
Additional comment
The remaining angles are supplementary to those inside the quadrilateral:
v = 180° -w = 107°
y = 180° -92° = 88°
z = 180° -66° = 114°
x = 51°