Answer:
a)
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b) [tex]z = 2.81[/tex]
c) Reject.
d) The p-value is 0.005.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Population 1:
Sample of 42, standard deviation of 3.3, mean of 101, so:
[tex]\mu_1 = 101[/tex]
[tex]s_1 = \frac{3.3}{\sqrt{42}} = 0.51[/tex]
Population 2:
Sample of 53, standard deviation of 3.6, mean of 99, so:
[tex]\mu_2 = 99[/tex]
[tex]s_2 = \frac{3.6}{\sqrt{53}} = 0.495[/tex]
H0 : μ1 = μ2
Can also be written as:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
H1 : μ1 ≠ μ2
Can also be written as:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error .
a. State the decision rule.
0.04 significance level.
Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b. Compute the value of the test statistic.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = \mu_1 - \mu_2 = 101 - 99 = 2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.51^2 + 0.495^2} = 0.71[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{2 - 0}{0.71}[/tex]
[tex]z = 2.81[/tex]
c. What is your decision regarding H0?
[tex]|z| = 2.81 > 2.054[/tex], which means that the decision is to reject the null hypothesis.
d. What is the p-value?
Probability that the means differ by at least 2, either plus or minus, which is P(|z| > 2.81), which is 2 multiplied by the p-value of z = -2.81.
Looking at the z-table, z = -2.81 has a p-value of 0.0025.
2*0.0025 = 0.005
The p-value is 0.005.
6x−36x2/ 6x simplified
Answer:
1x-72
Step-by-step explanation:
-36x2= -72
6x-72/6x
6x/6x=1x
1x-72
JoAnn is making jewelry. Set an expression that shows how much it will cost Joanne for the long length chain bracelet and for b beads that cost $0.30 each. Then find the total cost of the jewelry lol JoAnn uses 34 beads
Answer:
$0.30 x b
$10.20
Step-by-step explanation:
The equation is
$0.30 x b
Since we know JoAnn uses 34 beads, we can replace b with 34
$0.30 x 34 = $10.20
The Hu family goes out for lunch, and the price of the meal is $52. The sales tax on the meal is 6%, and the family also leaves a 20% tip on the pre-tax amount. What is the total cost of the meal?
Answer:
$65.52
Step-by-step explanation:
52 x 6% = 3.12. Multiply the price of the meal by the percentage of sales tax
52 x 20% = 10.4. Multiply the price of the meal by tip percent
$3.12 is the sales tax on the meal
$10.40 is the tip amount
$52 + $3.12 + $10.40 = $65.52
Add sales tax and the tip amount to the price of the meal to find the total
In your own words, describe the one thing that makes adding decimals different than adding whole numbers. Why is this important
Answer:
Step-by-step explanation:
One difference is that when adding decimals you have to be aware if you have to move it or is the numbers are lined up,while whole numbers you just add them with no worries just making sure your adding the number rights and getting the right answer .
what number I am if I am a factor of 90 but not a multiple of 6 and 9 i am greater than 10 but smaller than 20
Answer:
15
Step-by-step explanation:
15 can go into 90, 6 times. It is neither a multiple of 6 or 9. It is larger than 10 and smaller than 20.
X is y% of what number?
Answer:
42
Step-by-step explanation:
yeah-ya.......... right?
Enter your answer and show all the steps that you use to solve this problem in the space provided.
The ratio of boys to girls in Mrs. Williams’s class is 2 to 5. There are 15 girls in the class. What is the total number of students in Mrs. Williams’s class?
Answer:
It seems like the answer would be 21 students.
Step-by-step explanation:
5 times 3 is 15 so 15 girls
2 times3 is 6 so 6 boys
15+6=21
I hope this helps :))
The table shows the relationship between r and s, where s is the independent variable.
Which equation represents the relationship between r and s?
Answer:
burrito
Step-by-step explanation:
burrito
write an equation in standard form for a line that is (a) parallel (b) perpendicular to the line with an equation of Y= 3x -5 that passes through point (8,5)
1,256 balls divided by 13 games. About how many balls should each game get? Estimate answers are:
A. About 80
B. About 100
Those are the choices. 80 is not enough and 100 is too many. 90 or 96R8 not there. Ugh.
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week. About how many gallons of milk does the class drink in 10 weeks? Round your answer to the nearest tenth of a gallon if needed.
262.5 gallons of milk does the class drink in 10 weeks.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.
as, we know that
1 pint= 0.125 Galloon
So, 210 pints milk = 210 x 0.125 = 26.25 Galloon
Then, In 10 weeks amount of milk drink
= 26.25 x 10
= 262.5 Gallon
Learn more about Unitary Method here:
https://brainly.com/question/22056199
#SPJ2
Between which two integers does 7/3 lie?
Answer:
2 and 3
Step-by-step explanation:
7/3=2 1/3
So it lies between 2 and 3
2 1/3 is lesser that 3 but more than 2.
BRAINIEST IF CORRECT
The triangle below is equilateral. Find the length of side x in simplest radical
form with a rational denominator.
V12
Answer:
The side of an equilateral triangle equals:
2 * height / sqr root (3)
side = 2 * sqr root (12) / sqr root (3)
side = 2 * 2 * sqr root (3) / sqr root (3)
side x = 4
Step-by-step explanation:
Jack has 8 out of 10 questions correct. He said that he earned a 75% on his exam. Is he correct? Show why he is correct or incorrect.
Answer:
He is incorrect. He actually got an 80%
Step-by-step explanation:
[tex]\frac{8}{10}[/tex] = 80%
I hope this helps!
Explain how to graph a line when given the standard form Ax + By = C of a linear equation.
PLEASE HELP ME
Step-by-step explanation:
A= C. - By
x. ×
answer by a
huhuhu
6 times the sum of a number and ten is 60
What is the expression for this
Answer:
The equation is 6(x + 10) = 60, and the answer to the equation is 0
Step-by-step explanation:
Start by formatting the problem as [tex]6(x+10)=60[/tex]. Then, use the distributive property so that the problem is [tex]6x + 60 = 60[/tex]. After this, subtract 60 from both sides to isolate the variable, making the problem [tex]6x=0[/tex]. Finally, divide both sides by 0, which will get you an answer of [tex]x=0[/tex].
Find the area of the circle. Round to the nearest
tenth. Do not write units of measure.
Find the area of each circle. Use 3.14 for pi.
Answer:
452.16 cm
28.26 m
113.04 km
Step-by-step explanation:
The equation for area is r^2 π
where you square the radius and multiply by 3.14 or pi or how many digits you need to use.
For example, on the first question, you multiply the radius (12) by itself or square it to get 144.
Then you multiply 144 by 3.14 to get your first answer.
8 grade math part 2 help me
Answer:
287
Step-by-step explanation:
Reflex angle:
an angle greater than 180° and less than 360°
360-73=287
work out the surface area of this solid prism
Answer:
5220
Step-by-step explanation:
1- 20x36/2 is 360
(360 x 2 is 720)
2. 25x50 is 1250
3. 29x50 is 1450
4. 36x50 is 1800
720+1250+1450+1800 is 5220
Find the volume (in cubic yards) of a rectangular solid with length 3.8 yards, width 2.2 yards, and height 2.3 yards.
Answer:
19.228
Step-by-step explanation:
multiply 2.2*2.3*3.8 to get 19 yd^3
Question is in image below
A lamppost is 6 feet high and casts and 8 foot shadow. At the same time of day, a flagpole near the lamppost cast a 20 foot shadow. Using the properties of similar triangles, find the height, H, of the flagpole
Answer:
15 ft.
Step-by-step explanation:
I will assume that either both objects are standing straight. We can use similar triangles.
We can see that the side 8 is similar to the side 20, since they are both shadows. Therefore, we can set up an equation:
[tex]\frac{6}{8} =\frac{x}{20}[/tex]
we can cross multiply and get:
8x=120
solve for x:
x=15
Therefore, the lamppost must be 15 feet tall (unless it fell down but we won't talk about that)
can I have some help?
Answer:
[tex]x = \sqrt{58} [/tex]
Step-by-step explanation:
first, you should draw a line to separate the triangle from the rectangle
You can get the height if the triangle by saying 16-9
This will give you 7
The base of the triangle is 3 because the opposite side is given and the opposite sides of a rectangle are equal
Now that we have the measurements of the triangle we can use the Pythagorean theorem
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
[tex] {x}^{2} = {7}^{2} + {3}^{2} [/tex]
[tex] {x}^{2} = 49+ 9[/tex]
[tex] {x}^{2} = 58[/tex]
[tex]x = \sqrt{58} [/tex]
I have a Statistics question
Answer:
we're your question
Step-by-step explanation:
again please
Answer:
Yes
Step-by-step explanation:
what is it
Holly and Jimmy went shopping. For every $2
that Holly spent, Jimmy spent $5. If together
they spent $35, how much did Jimmy spend?
if you want it a a whole number, it would be for every 34$ 85 bucks for jimmy .
please help i only have a few minutes!! what are the measurements for 1 and 2?
Answer:
8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces
A student missed 15 problems on a mathematics test and received a grade of 80%. If all the problems were of equal value, how many problems were on the test?
Answer:
75 problems
Step-by-step explanation:
Let x be the number of problems on the test and x-15 be the number of correct answers the student got on the test:
(x-15)/x = 0.80
x-15 = 0.80x
-15 = -0.20x
75 = x
Therefore, there were 75 problems on the test
When a guy says i cheated just to let the world know what does it mean?
Answer ASAP
Answer:
He says that because he thinks ur cheating for attention. When they say you 'let the whole world know' that you`re unloyal and can be with any guy, without a care, it`s an insult.
Answer:
it means that he was dating another person while already dating
Step-by-step explanation:
it like when ur dating 2 people at one time without the other person knowing
If16 = x/20, then x=
Answer:
320
Step-by-step explanation:
16 × 20 = 320
To double check it, we insert 320 into the equation:
320 ÷ 20 = 16
2(7x-5)-6x+2=0 help me out
[tex]2(7x-5)-6x+2=0\\\\\implies 14x -10 -6x +2=0\\\\\implies 8x -8 =0\\\\\implies 8(x-1) =0\\\\\implies x -1 =0\\\\\implies x =1[/tex]
What is the greatest exponent in the expression 8x-x^2+9-3x^4+5x?
Answer:
4
Step-by-step explanation:
