A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the immune response of the recipients. They claim the variance in the immune response is 1.9. It is known that the immune responses follow a normal distribution. A random sample of 30 individuals were given the vaccine and their immune response recorded. It was found that they had a sample variance of 0.9. At the 5% significance level, test the hypothesis that the population variance of the immune response is equal to 1.9 against the two-sided alternative, that it is not. a. State the null and alternative hypothesis. b. Perform the hypothesis test. (You may use any of the methods we discussed that are appropriate for the problem.) c. State your decision. d. State your conclusion in full sentences.
Answer:
a
The null hypothesis is [tex]H_o : \ \sigma^2 = 1.9[/tex]
The alternative hypothesis is [tex]H_a : \ \sigma^2 \ne 1.9[/tex]
b
[tex]X^2 = 13.74[/tex]
c
The decision rule is
Reject the null hypothesis
d
The conclusion is
There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.
Step-by-step explanation:
From the question we are are told that
The variance is [tex]\sigma ^2 = 1.9[/tex]
The sample size is n = 30
The sample variance is [tex]s^2 = 0.9[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \ \sigma^2 = 1.9[/tex]
The alternative hypothesis is [tex]H_a : \ \sigma^2 \ne 1.9[/tex]
Generally the test statistics is mathematically represented as
[tex]X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }[/tex]
=> [tex]X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }[/tex]
=> [tex]X^2 = 13.74[/tex]
Generally from the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30 - 1[/tex]
=> [tex]df = 29[/tex]
Generally from the chi distribution table the critical value of [tex]\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}[/tex] at a degree of freedom of [tex]df = 29[/tex] is
[tex]X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7[/tex]
=> [tex]X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5[/tex]
Gnerally from the values obtained we see that
[tex]X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.
A plastic board that is 15 feet long is leaning against a wall
perpendicular to the ground. The point at which the wooden
board touches the wall is 12 feet above the ground. How far
away is the base of the board from the bottom of the wall?
feet
Answer:
9 ft
Step-by-step explanation:
a²+b²=c²a²+12²=15²a²+144=225225-144=81√81=9determine the coordinates
Answer:
Thus, the rule of a point P(x, y) reflected over the line y = -x
P(x, y) → P'(-y, -x)
we conclude that:
A(3, 4) → A'(-4, -3)B(3, 2) → B'(-2, -3)C(-1, 2) → C'(-2, 3)Step-by-step explanation:
We know that If a point P(x, y) is reflected over the line y = -x, the x-coordinate and y-coordinate tend to change places and the signs are reverses.
Thus, the rule of a point P(x, y) reflected over the line y = -x
P(x, y) → P'(-y, -x)
Thus, we conclude that:
A(3, 4) → A'(-4, -3)B(3, 2) → B'(-2, -3)C(-1, 2) → C'(-2, 3)HELP ME PLZ
A figure is shown in the image. What is the measure of the
highlighted angle?
А. 30
В. 60
С. 120
D. 65
Answer:
c is the correct answer i my guest
37:35-(32:24-10).2+√289=
Answer:
to simplify this it is 1295/1804
Step-by-step explanation:
An elm tree is 3 and 1/2 times as tall as an apple tree . The apple tree is 10 and 2/3 feet tall how tall is the elm tree
Answer:
111 1/3 feet tall
Step-by-step explanation:
Please help, solve a and b
Answer:
AE and BD use the same lines for both triangles so the angles for C are the same. this means that all the angles are congruent between both triangles.
Step-by-step explanation:
Answer:
The distance across the river d=175ft
Step-by-step explanation:
As◇ ABC& ◇ EDC are similar, BC/CD=AB/ DE
4x/7x=100/d
d=100×7/4=175
3
Lauren bikes
5
4
miles in
7
hours. How long does it take her to travel one mile?
if 2500 is invested for 4 years and 500 is earned in simple interest, then the yearly interest rate is?
Answer:
500/4=125
Step-by-step explanation:
Have a nice Day , I would appreciate it if you could mark my answer brainliest
Which equation represents the line whose slope is 2 and y-intercept is 6? a. 2y + 6x = 0 b. y = 6x + 2 c. y = 2x + 6 d. y + 2x = 6
Answer:
c. y=2x+6
Step-by-step explanation:
In slope intercept for (y=mx+b) m is the slope and b is the y-intercept.
what is the opposite of love
Answer:
opposite of love is hate
hope this answer will help you
Answer:
Hate is opposite of love
solve the following equation-7x-4y=-4 -9x-5y=-6
Answer:
[tex]\boxed{x = 4~~and~~ y = -6}[/tex]
.
Step-by-step explanation:
-7x - 4y = -4 (times 5) -35x - 20y = -20
-9x - 5y = -6 (times 4) -36x - 20y = -24
.
Eliminate both equations
[tex]-35x - 20y = -20[/tex]
-36x - 20y = -24
[tex]x = 4[/tex]
.
Substitute the value of x to one of equations
[tex]-7x - 4y = -4[/tex]
[tex]-7(4) - 4y = -4[/tex]
[tex]-28 - 4y = -4[/tex]
[tex]-4y = - 4 + 28[/tex]
[tex]-4y = 24[/tex]
[tex]y = \frac{24}{-4}[/tex]
[tex]y = -6[/tex]
Step-by-step explanation:
ib2j2nwj wjwjw wjw w wiw w akwbysks soshsiw sksns sks sos sisIyah lah s ais ssj sj
If ABCD is a rectangle, find the measure of angle ABD.
Answer: 31 degrees
Step-by-step explanation: Angle ABD and BDC are alternate interior angles, meaning that they are congruent. Therefore, the measure of angle ABD is 31 degrees.
The measure of angle ABD is 31°
What are alternate interior angles?Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure.
Given;
Angle CDB= 31°
Now
Angle ABD= Angle CDB (alternate interior angles)
Angle ABD= 31°
Therefore, angle ABD will be 31°
Learn more about angles;
https://brainly.com/question/7116550
#SPJ5
Which is the correct answer?
Answer:
I think it is B
Step-by-step explanation:
I cannot be sure about it though as I am just started learning about it at school myself. Plus, I can't read the writing that well 'cause I think the screen is slightly sideways. Hope this helps! :)
I need help please I have to finish this
Answer:
x = 80 degrees
y = 25 degrees
Step-by-step explanation:
First find angle BCA.
We know a line is 180 degrees, and angle BCD is 130. So 180-130 = 50 degrees for angle BCA.
Since it is isosceles (two lines on both sides of triangle ABC) this means the bottom two angles are the same. Now we know the two angles to find missing angle X.
50+50+ x = 180 degrees
x= 180 - 100 = 80 degrees
Next we know triangle BCD is isosceles, so angle BDC and angle CBD are the same. We know the third angle is 130 degrees.
So 180 - 130 = 50 degrees split between two angles that are the same. So one angle is 50/2 = 25 degrees.
please give thanks by clicking the heart button :)
what is the percent of change from 300,000 to 30,000 its 90
Answer:
-90%
Step-by-step explanation:
please help me step by step
Answer:
should be just be like doubling everytime
Step-by-step explanation:
6 water and 4 powder
12 water 8 powder
18 water 12 powder
it's the same ratio so it should taste the same, like 3 water and 2 powder is going to taste the same as 18 water and 12 powder
Suppose ALI was told that relative to the other scores on a NTS test, his score was the 95th percentile i.e., his percentile score is 95. How do we interpret it?
Please answer i don't have muc time
PLEASE HELP ME OUT FAST MULTIPLE CHOICE IF YOU DOMT KNOW PLEASE DONT RIGHT ANYTHING!
Answer:
B
Step-by-step explanation:
When you are finding the solution of two lines on a graph, you look at the intersection point and that is the answer. On the given graph, both lines intersect at (4, -3). Thus, that is the solution.
Best of Luck!
!!!!!!!!!!!!!!!!!! help
Answer:
option 1
Step-by-step explanation:
It's given in the question that
a (first term of an A.P.) = 14
d (common difference between terms of A.P.) = -3
So,
2nd term will be = a + d = 14 + (-3) = 11
3rd term = a + 2d = 14 + 2×(-3) = 8
4th term = a + 3d = 14 + 3×(-3) = 5
All these terms are matching with option 1. So, option 1 is the correct option
if f(x)=3 what is x?
Answer:
0
Step-by-step explanation:
srry if it's wrong :/
Please help me slove this problem
-6x + 4 = -20
Answer:
x = 4
Step-by-step explanation:
-6x + 4 = -20, Subtract 4 on both sides
-6x = -24, Divide -6 on both sides
x = 4
The coordínates of point A in a cordinate grid are -2,-3point A is reflectes Across the Y axis to obstinada point B and across the X a is tonobtain point C
Answer:
B(2,3),C(2,-3)
Step-by-step explanation:
On y-axis symmetry有手就行
Find the slope of the line that passes through the two points given.
(-3, 1) and (-1,5)
Answer:
2/-3
Step-by-step explanation:
3. (03.01 LC) The domain of the following relation: R: {(-4, 8), (8, 10), (5, 4), (1, 6), (5, -9)} is (1 point) {8, 10, 4, 6, -9) {-4, 1, 5, 8) O {-4, 8, 5, 1, 5} No domain exists
Answer:
{-4, 1, 5, 8}
Step-by-step explanation:
The domain of a relation are all of the inputs (or x-values) of it.
Identify the x-values shown.
{(-4, 8), (8, 10), (5, 4), (1, 6), (5, -9)}
{-4, 1, 5, 8} is the domain of the relation.
Hope this helps.
Don't worry gotten it
Answer:
Step-by-step explanation:
Ok :)
Complete the sentence. The x-distance between two points tells you
Answer:
distance
Step-by-step explanation:
Step-by-step explanation:
The key to finding the distance between two points is to remember that the geometric definition of subtraction is the distance between the two numbers as long as we subtract the smaller number from the larger.
8 pencils for 14 dollars
Answer:
1 pencil will be for 1.75 $
Answer:
$1.75 for each pencil.
Step-by-step explanation:
if you're asking the price for each pencil then its 1,75 for each because 8 multiplied by 1.75 is 14 :))
what is the answer for this( 7 3 x ∛27 - 2) x 1 5 + √81
Answer:
5208
Step-by-step explanation:
(73 x ³√27 - 2) x 15 + √81
(73 x 3 - 2) x 15 + 9
(219 - 2) x 24
217 x 24
5208