The U.S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 24.2 gallons per year. A random sample of 101 people in the United States shows that the mean coffee consumption is 23.5 gallons per year with a standard deviation of 3.2 gallons. At α=0.05, can you reject the claim? Using a P-value, evaluate the claim. Using Rejection Regions for a z-test, evaluate the claim.

Answers

Answer 1

Answer:

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 24.2 \ gallons \ per \ year[/tex]

    The sample size is  n  =  101

     The sample mean is  [tex]\= x = 23.5 \ gallons\ per\ year[/tex]

     The standard deviation is  [tex]\sigma = 3.2 \ gallons[/tex]

The null hypothesis is  [tex]H_o : \mu = 24.2[/tex]

 The alternative hypothesis is [tex]H_a : \mu \ne 24.2[/tex]

Generally the test statistics is mathematically represented as    

               [tex]z = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]

=>             [tex]z = \frac{ 23.5 - 24.2 }{ \frac{ 3.2}{ \sqrt{ 101} } }[/tex]  

=>             [tex]z = -2.198[/tex]

From the z table  the area under the normal curve to the left corresponding to    -2.198  is  

         [tex]P(Z < -2.198 ) = 0.013975[/tex]

Gnerally the  p-value is mathematically represented as

         [tex]p-value = 0.013975 * 2[/tex]

=>      [tex]p-value = 0.02795[/tex]

From the value obtained we have that  [tex]p-value \ < \ \alpha[/tex] hence  

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Using the Rejection Regions for a z-test method

Generally from the z table  the critical value  of [tex]\frac{\alpha }{2}[/tex]  is  

     [tex]z_{critical} = \pm 1.96[/tex]

Not we are using  [tex]\frac{\alpha }{2}[/tex]  because it is a two - tailed test

   Now comparing the critical value and the test statistics we see that the

region covered by  the test statistics (i.e [tex]2.198 < z < -2.198[/tex])   is greater than the region covered by  the critical value  (i.e [tex]1.96 < z < -1.96[/tex])

Hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  


Related Questions

Which is the best description for the graph?
O The graph is increasing everywhere.
O The graph is decreasing everywhere.
O The graph is increasing, then decreasing.
O The graph is decreasing, then increasing.

Answers

i think it’s the graph is decreasing everywhere
The graph is decreasing everywhere.

A mail carrier travels at 15 miles per hour through a neighborhood. Which table
represents the distance the mail carrier travels in x hours?
2
G
H
0 1 3
yo 16 18
0 24
yo 30 55
x 135
y 15 45 75
x 134
y 15 40 55

Answers

Answer:

Step-by-step explanation:

the table is not copied correctly, I assume

the mail carrier will travel a distance of 15x

( Need Help Now!!!!!!) Noelle has four times as many apples in her grocery bag as her friends Dakota and Kylie combined. Dakota has 1 apple in her bag. Noelle has 16 apples in her bag. How many apples does Kylie have in her grocery bag? The equation 4(x + 1) = 16 models this situation. Which choice shows the sequence of operations needed to solve this problem, using both arithmetic and algebra?​

Answers

Answer:

3 Apples

Step-by-step explanation:

3 + 1 = 4, 4 x 4 = 16 Apples :D

Answer:

The answer is 6 Apples

Step-by-step explanation:

You have to ad 3+2 equals 4 then 4 times 4  is 16 so the answer is 16 apples.

3 + 1 = 4, 4 x 4 = 16 Apples

I need help with this please.

Answers

Answer:

CCCC.

Step-by-step explanation:

what are all values of x for which the series shown converges? ​

Answers

Answer:

One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:

Iaₙ₊₁I < IaₙI

This means that the absolute value of the terms must decrease as n increases.

Then we must have:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}}[/tex]

We can write this as:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2 )^{n+1}}{(n + 1)*3^{n+1}} = \frac{(x -2)^n}{(n + 1)*3^n} * \frac{(x - 2)}{3}[/tex]

If we assume that n is a really big number, then:

n + 1 ≈ 1

And we can write:

[tex]\frac{(x -2)^n}{n*3^n} > \frac{(x -2)^n}{(n)*3^n} * \frac{(x - 2)}{3}[/tex]

Then we have the inequality

[tex]1 > (x - 2)/3[/tex]

And remember that this must be in absolute value, then we will have that:

-1 < (x - 2)/3 < 1

-3 < x - 2 < 3

-3 + 2 < x < 3 + 2

-1 < x < 5

The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.

Scott has a bag with 144 pieces of candy in it. He gives his sister 25% of the candy. How many pieces of candy does Scott give his sister?

Answers

Answer:

Step-by-step explanation:

Scott has 144 pieces of candy

25% is one 4th

144/4=36

he gives to his sister 36

Answer:

Scott gives his sister 36 peices of candy

Step-by-step explanation:

Enuncia 5 vectores que pertenecen a un mismo sub espacio

Answers

Answer:

what?

Step-by-step explanation:

Which ratio is larger, 10 to 15 or 14 to 21?

Answers

Answer:

I am pretty sure that is it 14 to 21

Step-by-step explanation:

Sorry if i am wrong

THE CORRECT ANSWER IS 12 FAVORS!!

Answers

Answer:

yes the answer in 12 fpavers

Step-by-step explanation:

wa

Solve the equation.
-5r-1=7r+5

Answers

Answer:

r=-1/2

Step-by-step explanation:

(-5*-1/2=2.5)( 2.5-1=1.5) (7x -1/2= -3.5)-3.5+5 =1.5

Javier teaches yoga classes at his community center. In a 60-minute class last night, he taught 30 poses. Today, he has a 30-minute class. If he teaches at the same rate, how many poses will Javier teach in today's class?

Answers

Answer:

15

Step-by-step explanation:

fifteen is half of 30

b) 7p + 6q- 2p + q = ?

Answers

[tex]7p + 6q - 2p + q \\ = (7p - 2p) + (6q + q) \\ = 5p + 7q[/tex]

Answer:

5p+7q is the answer

Step-by-step explanation:

The sum of two integers is 9 their difference is 5 what are the 2 integers

Answers

the two integers are 7 and 2

I NEED HELP PLZ ITS FOR MY FINAL

Answers

Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that answers. Pls help me and explain why it’s that Pls help me and explain why it’s that answers. answers.

Let g (2) = 22 – 5 and h (2) = 22 +1.
Find (g+h) (2)

Answers

Answer:

23 + 17 = 40 :)

Solve – 4y – 10 = 4(y - 3)

Answers

Answer:

y= 1/4

Step-by-step explanation:

Answer:

y=-7/8

Step-by-step explanation:

-4y-10=4y-3

add 10 on both sides

-4y=4y+7

subtract the four on the right from both sides

-8y=7

divide -8 on both sides

answer: -7/8

Derek weighs 155 pounds and drives a utility vehicle that can carry no more than 220 pounds. He plans to use his utility vehicle to haul blocks to his backyard. Which inequality shows the number of 3 pounds, b, Derek can haul at one time on his utility vehicle

Answers

By the looks of this the answer is E

Derek weighs 155
155+220

PLEASE HELP!! IT DUE TODAY! im begging you please help me out

Answers

Answer:

11(2r+1)

16(2t+1)

9(4+c)

14(3k+2)

Step-by-step explanation:

no real way to explain besides factor them and take the largest common factor out

Answer:

1) 11(2r+1)

2) 16(2t+1)

3) 9(4+c)

4) 14(3k+2)

Step-by-step explanation:

Factor these expressions, find the GCF and divide the GCF on both the numbers, keep the numbers and put them in parenthesis and put the GCF on the outside of the parthensesis.

what is greater -.89 or .4

Answers

Answer:

.89

Step-by-step explanation:

.89 is greater because it is closer to a whole than .4, which makes .89 greater.

A salesperson at a jewelry store earns 5% commission each week last week heidi sold $540 worth of jewelry how much did she make in the commission how much did the jewelry store make from her sales

Answers

Answer: $27

Step-by-step explanation:

$540x.05=$27

Answer:

Heidi made $27 from commision; And the store made $513 (i had this question my self on Saavas)

Step-by-step explanation:

1. 540x0.05=27

2. 540-27= $513

So the store made 513 dollars and heidi made 27 dollars

Which of the following represents the measures of all angles coterminal with a -220° angle?
O 360 + 140n, for any whole number n
O 360 + 140n, for any integer n
O 140 + 360n, for any whole number n
O 140 + 360n, for any integer n

Answers

Answer n 9 Explanation 140 degrees is the measure of each angle and the sum of ... So degrees and radians are related by the following equations 360 2 ... Measure angles in whole number degrees using a protractor.

The measurement of all angles co-terminal with a -220° angle is represented by 140+ 360 n, for any integer number n.

What are Co-terminal angles?

These are the angles which shares the same initial line or terminal side. They are obtained by adding or subtracting 360° from the given angles.

Given, angle is -220° then its one positive co-terminal angle= -220°+360 = 140°

So, 140° is a positive co-terminal angle of -220°.

Therefore, co-terminal angle must be the type of 140°+360° n,

Learn more about  Co-terminal angles.

https://brainly.com/question/14692520

#SPJ5

PLEASE HELPPPP
Find the equation of the linear function represented by the table below in slope-
intercept form.
X
O
1
2
3
4
y
6
14
22
30
38
Answer: y =
Submit Answer

Answers

Answer:

yo done so easy

Step-by-step explanation:

the answer is y=8x + 6

30 is 2/3 of what number

Answers

Answer:45

Step-by-step explanation:

Key Word:of

30*2/3 = 45

Answer:

Step-by-step explanation:

let the number be x.

then,

2/3 of x = 30

=> 2/3x = 30

=> x = 30 × 3/2

=> x = 45

so, the required number is 45 .

hope it helps...!!!

A and B are independent events.
PA) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
B. 0.6
O c.0.4
D. Not enough information

Answers

Answer:

not enough information

Answer:

It's 0.6

Step-by-step explanation:

question is in the picture pls help me. much appreciated

Answers

Okay for a diagonal length it isn’t to hard. So 2y-3 is half of the 12 diagonal

So 2y-3+ 2y-3 = 12 or 4y-6= 12
Add 6 to both sides 4y=20
Divide 4 from both sides y=5

Hope this helps

Brandi wants to participate in an after-school program. She has to choose between one art class, three dance classes, bwo gymnastics classes, or three sports casses. She cannot decide, so she writes the name of each class on a slip of paper and draws one slip out of a bag. What is the probability that she does not draw a dance class?​

Answers

Answer:

Step-by-step explanation:

Its 1/3 just put that it will be right I promise

Which equation can be used to solve for x in the following diagram?
(6z- 15)°
Choose 1 answer.
z= (6z-15)
O z-(6z-15) = 90
O z+(6z- 15) = 90
4 of 7

Answers

Answer:

I'm answering this for points

The average combined SAT score for students at Brookstone High was 1000 in 2003, 1100 in 2004, 1210 in 2005, and 1331 in 2006. Predict the SAT score for Brookstone seniors in 2007. Explain your answer.

Answers

1, 441 in 2007 because it is going in a pattern add 100 plus 10 to get your 2005 answer so then I add 100 plus 10 plus 11 for 12,10 to get 1331 . so the answer is 1,441

Total Cost of Computer Repair = $1,444.50

Shipping = 2 percent of Total Cost

If Sarah wanted to include a 15 percent gratuity, based on the total cost of the computer repair, excluding shipping, how would you find her new total cost?

Answers

Answer:

Its D

Step-by-step explanation:

0.02 ($1,444.50)

Answer:

D

Step-by-step explanation:

The monthly expenditures on food by single adults in one city are monthly distributed with a mean of $410 and a standard deviation of $70

Answers

Answer:

is the whole question asked?

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