According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:
The value of the test statistic is z = 1.65.The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
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.
Before:
Average of 0.250 in 56 at bats, so:
[tex]p_B = 0.25[/tex]
[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]
After:
Average of 0.44 in 25 at bats, so:
[tex]p_A = 0.44[/tex]
[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]
Test if there was improvement:
At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:
[tex]H_1: p_A - p_B > 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.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.19 - 0}{0.1149}[/tex]
[tex]z = 1.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
A similar question is found at https://brainly.com/question/23827843
Nick needs one more class to complete his schedule. There are 5 writing classes, 3 history classes, and 4 mathematics classes that can fit into his schedule. If Nick chooses a class at random, what is the probability that he chooses a history class? Give your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Probability = 3/(5+3+4)
= 3/12 or 1/4
a gift wrapping store has 8 shapes of boxes, types of wrapping paper, and 12 different bows. How many different gift-wrapping options are available at this store?
Answer:
This sum is related to fundamental principal of counting which states that if one thing is happen in m different ways and other thing happen in n ways, Then both thing will happen in mn ways. We shall use its generalised form.
In given sum, Number of shapes of boxes=8
Number of types of wrapping papers=14
Number of different bows=12
As gift wrapping includes three items Therefore by fundamental principal of counting, number of different gift wrapping option =8×14×12= 1344
Step-by-step explanation:
Answer:
768
Step-by-step explanation:
8 boxes* 8 paper * 12 bows
768 different combinations
Little’s Law Firm has two lawyers. Customers arrive randomly at an average rate of 1 per hour. Service times have a mean of 60 minutes and a standard deviation of 15 minutes. What is the average number of customers in Little’s Law Firm?
Answer:
[tex]X=4[/tex]
Step-by-step explanation:
From the question we are told that:
Number of lawyers [tex]N=2[/tex]
Arrival Rate [tex]r= 1 per hour[/tex]
Mean [tex]\=x=60min[/tex]
Standard deviation [tex]\sigma= 15[/tex]
Generally, the equation for average number of customers in Little’s Law Firm
is mathematically given by
[tex]X=Arrival rate (r) * Average service time (t)[/tex]
[tex]X=1*\frac{60}{15}[/tex]
[tex]X=4[/tex]
At the annual music festival, the number of Bayview Middle School students competing in the band, chorus, and orchestra competitions is 14, 13, and 17 students respectively. 4 students will compete in all three competitions. 5 students will compete in band and chorus competitions. 6 students will compete in band and orchestra competitions. 7 students will compete in the chorus and orchestra competitions. How many students from Bayview Middle School competed in the music festival
Answer:
30 students
Step-by-step explanation:
The problem above can be solved using a Venn diagram :
Using the information given :
The number of students competing :
Band and chorus only (BnC) only = 5 - 4 = 1
Band and Orchestra (BnO) only = 6 - 4 = 2
Chorus and Orchestra (CnO) only = 7-4 = 3
Chorus only (C) = 13 - (1+4+3) = 5
Band only (B) = 14 - (1+4+2) = 7
Orchestra only (O) = 17 - (2+4+3) = 8
The Total Number of Bayview students who competed :
(8+7+5+3+2+1+4) = 30
Which of the following theorems verifies that angle DEF ~ angle XZY?
Step-by-step explanation: In this problem, notice that we're only given one pair of congruent angles, the 90 angles, but remember that the sum of the measures of the angles of a triangle is 180°.
So we can determine that the measure of the missing angle
of our first triangle is 40° because 90 + 50 + 40 = 180.
Now we have two pairs of congruent angles,
the 40° angles, and the 90° angles.
Therefore, since two of the angles of one triangle are congruent to
two of the angles of the other triangle, we can say that yes, the
triangles are similar by the Angle-Angle Similarity Postulate (AA~).
If a=2b=2c find the value of each.
Answer:
b=a/2
c=a/2
b=c
a=2b and a=2c
. A swimming pool was filling with water at a constant rate of 200 gallons per hour. The pool had
50 gallons before the timer started. Write an equation in standard form to model the situation, then
find the amount of water in the pool after 2 hours and 15 minutes.
PLEASE HELP
-1/2m=-9
Show your work in details if you can, I have a hard time understanding this.
Answer:
m=18
Step-by-step explanation:
-1/2m=-9
-m=-18
m=18
[tex] \begin{cases} \\ \\ \large\bf{\green{ \implies}} \tt \: - \: \frac{1}{2} \: m \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{1 \: m}{2} \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 9 \: \times \: 2 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 18 \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{ \cancel- 18}{ \cancel - 1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{18}{1} \\ \\ \large\bf{\green{ \implies}} \tt \: m = \: 18 \: \\ \\ \end{cases}[/tex]
Please answer spammers will be reported
Answer:
Answer is number 2 as twice of 2 is 4 and double of 4 is 8 and 8+2=10
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Pls help me plakalalla
Answer:
#10 x = 6
Step-by-step explanation:
Not sure how many questions you needed answered. The line segments DE + EF = DF
4x - 1 + 9 = 9x - 22
solve for x
x=6
please help! 50 points!
Answer:
a) forming a bell
b) 5
c) 4.7
d) mean
is the correct answer
pls mark me as brainliest
In a recent year, 34.1% of all registered doctors were female. If there were 58,300 female registered doctors that year, WHOL ML
doctors?
Round your answer to the nearest whole number.
Blair & Rosen (B&R) plc is a U.K. based brokerage firm that specializes In building investment portfolios designed to meet the specific needs of its clients who are mostly private investors willing to invest their r savings in stocks and shares. One client who contacted B&R recently has a maximum of $500,000 to invest. The company`s investment advisor has decided to recommend the portfolio consisting of two investment funds: An internet fund where the companies are all active in internet businesses of one kind or another and the blue-chip fund which is more conservative and traditional. The internet fund has a projected annual return over the next few years of 12 %, while the blue-chip fund has a projected annual return of 9%. The investment advisor has decided that at most, $350,000 of the client`s funds should be invested in the internet fund. B&R services include risk rating for each investment alternative. The internet fund which is more risky of the two alternatives has a risk rating of 6 for every thousand dollar invested while the blue-chip fund has a risk rating of 4 per thousand dollar invested. So, for example, if $10000 is invested in each of the two investments funds, B&R risk rating for the portfolio would be 6(10) + 4(10)= 100. Finally B&R has developed a questionnaire to measure each client`s risk tolerance. Based on the responses, each client is classified as conservative, moderate or aggressive investor. The questionnaire results have classified the current client as a moderate investor. B&R recommends that a client who`s a moderate investor limit his or her portfolio to a maximum risk rating of 240. You have been asked to help the B&R investment advisor.
What is the recommended investment portfolio for this client?
What is the annual return for the portfolio?
a) The Investment portfolio consisting of the internet fund and Blue chip fund would be the recommended Portfolio for a moderate risk investor
b) The annual return for the portfolio is = $5100 ( Calculated using the excel formula sheet attached below )
The best/recommended investment portfolio for this client is the Investment portfolio consisting of the internet fund and Blue chip Fund because the Portfolio consists of a lower risk rating of 4 for every thousand which is conservative, and also an Internet fund which has a risk rating of 6 for every thousand ( aggressive ). The combination of a high and low risk investment fund in a portfolio results to an average/moderate risk portfolio.
Calculating the Annual return for the portfolio ( using the excel sheet below)
Model Internet fund Blue chip fund
Amount to invest 20 30
Total amount invested = 20 + 30 = 50
Total risk rating = 240
Total return = 5.1
hence: The recommended investment portfolio for this client is the Blue chip fund and the total return on the portfolio = $5100 applying the excel formulae attached below
Internet Fund = $20,000
Blue chip fund = $30,000
Learn more : https://brainly.com/question/7589262
Evaluate the expression: y – y ÷ 1 + x Use x = 7 and y = 3
Hi ;-)
[tex]x=7 \ and \ y=3\\\\y-y:1+x=3-3:1+7=3-3+7=0+7=\boxed7[/tex]
Divide 3 2/3 ÷ 2 1/3. Simplify the answer and write it as a mixed number.
Jessica works 5 days a week at a factory 7.5 miles from her home.
She travels to and from work in her car which has a fuel consumption of 30 miles per gallon.
Fuel costs £1.14 per litre and there are 4.55 litres in a gallon.
It costs £2.50 to park her car each day.
Rounded to the nearest £1, how much does it cost Jessica to travel to work in her car for a week?
Answer:
£25
Step-by-step explanation:
total distance travelled per week = 2 * 7.5 * 5 = 75
amount of fuel used = 75/30 = 2.5 gallons = 11.375 litre
cost of fuel = 11.375 * 1.14 = 12.9675
total cost = 5(2.5) + 12.9675 = 25.4675 ~~ 25
A manufacturing company plans to coat the entire exterior of a cylindrical shipping container with a 0.075-mm layer of special rust proof paint. The cylinder has a radius of 5 cm and height of 12 cm. The paint costs $0.35 per cubic centimeter. What is the cost of the paint for each cylinder?
Answer:
534.07cm² * 0.35=186.9245 dollar
Calculate a high estimate for each. Show your work?81×37
Step-by-step explanation:
2997
81
×
37
=2997
it just a simple calculation just multiply the numbers
An Image point after a 180° rotation Is Z(3, 7). What were the coordinates of the pre-Image point?
Z-3-7)
2173)
27-3)
21-7-3)
Answer:
Does the answer help you?
x^2+ 8x+ How to make it a perfect square
Hey there! I'm happy to help!
A perfect square means that this equation is the product of two identical binomials (this is a quadratic due to the x^2, so it is made up of two binomials) so for example (x+2)(x+2) would be x^2+4x+4 which is a perfect square as you can square root x^2+4x+4 and (x+2) and not some other crazy thing.
So, we have most of the final quadratic but we need the one constant number on the end. How are we going to find it?
If you are familiar with quadratics, you probably know that adding the two numbers in the binomials gives you b and multiplying them gives you c with a quadratic ax^2+bx+c because of the foil method (if you don't know what that it is, just comment on the answer and I can explain it to you). Basically what that tells us is that our binomial numbers are going to add up to be eight (and we also know that they must be the same number as we want a perfect square). We know that 4+4 is equal to eight, so that means that our binomial pair will look like this:
(x+4)(x+4)
And we also know that multiplying them gives you c, so 4×4=16 and there is our c. We just throw it on at the end of the equation.
x^2+ 8x+16
If you have any more questions, feel free to ask me. Have a great day! :D
Here are some photos of my math home work please show some work.
Answer:
I can answer 2-19.
Step-by-step explanation:
The first equation is x=0.
the second equation has no solution.
The area of a rectangle is given by the trinomial y^ 2 +4y-45. If the length of the rectangle is y + 9 , what is the width of the rectangle?
Step-by-step explanation:
Area of rectangle =L×W
Width =Area
[tex]w idth= \frac{area \ }{length} \\ \\width = \frac{ {y}^{2} + 4y - 45}{y + 9} \\ \\ = \frac{(y - 5)(y + 9)}{(y + 9)} \\ \\ width = y - 5[/tex]
Mr. Lock bought 6 quarts of oil for his car. He spent $16.02. How much was each quart of oil?
Answer:
2.67
Step-by-step explanation:
To solve this problem do 16.02 / 6.
I hope this answer helps you out! Brainliest woudl be appreciated.Một cuộc điều tra tại một đô thị cho kết quả: 20% dân số dùng một loại sản phẩm A, 50% dân số
dùng một loại sản phẩm B, 15% dân số dùng cả hai loại A và B. Chọn ngẫu nhiên một người dân
trong đô thị đó, tìm xác suất để:
a. Người đó dùng sản phẩm A hoặc B.
b. Người đó không dùng sản phẩm A cũng không dùng sản phẩm B.
c. Người đó chỉ dùng đúng một trong hai loại sản phẩm A hoặc B.
d. Người đó chỉ dùng duy nhất sản phẩm A.
Please help
Simple geometry / trig problem
Answer:
b, c, dStep-by-step explanation:
a. tan 30/ sin 30 = (sin 30/cos 30) / sin 30 = 1 / cos 30, no
b. cos 30 = √3/2, yes
c. cos 60 tan 60 = cos 60 (sin 60/cos 60) = sin 60 = cos 30, yes
d. sin 60 = cos (90 - 60) = cos 30, yes
[tex]\bf{b.}\ \ \it cos30^o=\dfrac{\sqrt3}{2}\ \ (True)\\ \\ \bf{d.}\ \ \it sin60^o=cos(90^o-60^o)=cos30^o\ \ (True) \\ \\ \bf{c.}\ \it cos60^o\cdot tan60^o=cos60^o\cdot\dfrac{sin60^o}{cos60^o}=\dfrac{cos60^o}{cos60^o}\cdot sin60^o=1\cdot sin60^o=cos30^o\ (T)\\ \\ \\ \bf{a.}\ \ \it \dfrac{tan30^o}{sin30^o}=tan30^o\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{cos30^o}\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{sin30^o}\cdot\dfrac{1}{cos30^o}=\\ \\ \\ =1\cdot\dfrac{1}{cos30^o}=\dfrac{1}{cos30^o}\ \ne\ cos30^o[/tex]
kaiden and her brother both open savings accounts. each begin with a balance of zero dollars. for every two dollars that kaiden saves in her account, her brother saves five dollars. if kaiden saves 300 dollars how much did her brother save
The ratio is 2:5
Kaiden saves=300$Let her brother saves xATQ
[tex]\\ \sf\longmapsto \dfrac{300}{x}=\dfrac{2}{5}[/tex]
[tex]\\ \sf\longmapsto 2x=300(5)[/tex]
[tex]\\ \sf\longmapsto 2x=1500[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{1500}{2}[/tex]
[tex]\\ \sf\longmapsto x=750\$[/tex]
For the function G defined by G(x) = 5x + 3, find G(2)
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
express 111 as a sum of two primes
Answer:
2 + 109 = 111
Step-by-step explanation:
.............
Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as elena. Link drank twice as much as Jada. Did jada drink more or less then elena? Explain how you know
Answer:
Step-by-step explanation:
3\4 bc on a nuberline it would be 3 3\4
I--I----(etc)
so yeah hope i helped
Laura made $273 for 13 hours of work.
At the same rate, how much would she make for 17 hours of work?
sl
X
$
?
I
