1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
galina1969 [7]
3 years ago
13

The average yield of the standard variety off soybeans per acre on a farm in a region is 48.8 bushels per acre, with a standard

deviation of 12.0 bushels per acre. We have developed a new variety of soybean that we believe will have a higher mean yield per acre. To test this, we draw a random sample of 36 one-acre plots from the region, plant the new variety of soybean, and compute the sample mean yield per acre. The sample mean yield per acre is 53.4 bushels. Carry out the test at the 0.01 level of significance. (You can assume that yields per acre are approximately normally distributed.) Follow all steps clearly and write a clear conclusion. Include all necessary conditions check and show all your working.
Mathematics
1 answer:
I am Lyosha [343]3 years ago
3 0

Answer:

z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3  

p_v =P(Z>2.3)=1-P(Z  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.  

Step-by-step explanation:

1) Data given and notation  

\bar X=53.4 represent the sample mean

\sigma=12 represent the population standard deviation assumed

n=36 sample size  

\mu_o =48.8 represent the value that we want to test  

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 48.8, the system of hypothesis would be:  

Null hypothesis:\mu \leq 48  

Alternative hypothesis:\mu > 48  

Since we assume that know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{53.4-48.8}{\frac{12}{\sqrt{36}}}=2.3  

4)P-value  

Since is a right tailed test the p value would be:  

p_v =P(Z>2.3)=1-P(Z  

5) Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 48.8 at 1% of signficance.  

You might be interested in
Equivalent expression 7s+8t+10s+12t
Dahasolnce [82]

Answer:

17s+20t

Step-by-step explanation:

4 0
2 years ago
Combine like terms to simplify the expression below:<br> 14x - (2x -y) -y STEP BY STEP PLEASE
dimulka [17.4K]
14x - (2x - y) - y
14x + (-1(2x - y)) - y
14x + (-1(2x) - 1(-y)) - y
14x + (-2x + y) - y
14x + 1(-2x + y) - y
14x + 1(-2x) + 1(y) - y
14x - 2x + y - y
14x - 2x
12x
8 0
2 years ago
Read 2 more answers
How to find out the value of the lettered sides
umka2103 [35]

Step-by-step explanation:

  • a

sin 46°= a/12.8

a = sin46° * 12.8 = 9.20

  • b

cos59°=b/16.8

b = cos59°*16.8 = 8.65

3 0
3 years ago
Read 2 more answers
A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sa
IceJOKER [234]
Check it out .....


hope it helps...if any trouble occurs ...punch it on face.....haha kidding.....feel free to ask me

7 0
2 years ago
UPS charges $6.00 for the first pound, $1.00 for the second pound, and $0.15 for each additional pound. FedEx charges $4.00 for
Pavlova-9 [17]

Answer:

12 pounds

Step-by-step explanation:

We we need to write equations to represent the situation in this problem.

x=weight of package

UPS cost=6+1+0.15(x-2)

UPS cost=6+1+0.15x-0.3

UPS cost=6.7+0.15x

FedEx cost=4+2+.25(x-2)

FedEx cost=4+2+0.25x-0.5

FedEx cost=5.5+0.25x

Next, we can set the two equations equal to each other to solve for x.

6.7+0.15x=5.5+0.25x

6.7+0.15x-5.5=5.5+0.25x-5.5

1.2+0.15x-0.15x=0.25x-0.15x

1.2/0.1=0.1x/0.1

x=12

It takes 12 pounds for the UPS and FedEx packages to cost the same amount to ship.

8 0
3 years ago
Other questions:
  • Which linear inequality is graphed with y&gt;-x-2 to create the given solution set?
    7·1 answer
  • Find all zeros of f(x)= x^3-4x^2-5x+20
    14·1 answer
  • How many elements make up matter
    7·2 answers
  • PLEASE HELP I WILL GIVE BRAINLIEST IT DUE IN 1 HOUR
    6·1 answer
  • Use the Pythagorean theorem to classify the triangle
    13·2 answers
  • QN (b) plz solve it fast ​
    15·1 answer
  • Will 5 star worth 76pts
    13·1 answer
  • Which function describes the arithmetic sequence shown?<br> 3,1,-1,-3-5.-7...
    10·1 answer
  • What is the slope for each for each line<br><br> y=1/2x-4<br> y=2x-3
    6·2 answers
  • Draw a tree diagram to represent the following scenario. You choose a random letter from the word SANDWICH. How many possible ou
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!