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
densk [106]
3 years ago
5

A dairy farm uses the somatic cell count (SCC) report on the milk it provides to a processor as one way to monitor the health of

its herd. The mean SCC from five samples of raw milk was 250,000 cells per milliliter with standard deviation 37,500 cell/ml. Test whether these data provide sufficient evidence, at the 10% level of significance, to conclude that the mean SCC of all milk produced at the dairy exceeds that in the previous report, 210,250 cell/ml. Assume a normal distribution of SCC.
Mathematics
1 answer:
Eva8 [605]3 years ago
6 0

Answer:

t=\frac{25000-210000}{\frac{37500}{\sqrt{5}}}=2.37  

p_v =P(t_{4}>2.37)=0.038  

If we compare the p value and a significance level assumed \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is higher than 210250 at 5% of significance.  

Step-by-step explanation:

Data given and notation

\bar X=250000 represent the sample mean  

s=37500 represent the standard deviation for the sample

n=5 sample size  

\mu_o =210250 represent the value that we want to test  

\alpha=0.1 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is higher than 210250, the system of hypothesis would be:  

Null hypothesis:\mu \leq 210250  

Alternative hypothesis:\mu > 210250  

Compute the test statistic  

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-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".  

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

t=\frac{25000-210000}{\frac{37500}{\sqrt{5}}}=2.37  

Now we need to find the degrees of freedom for the t distirbution given by:

df=n-1=5-1=4

Conclusion

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

p_v =P(t_{4}>2.37)=0.038  

If we compare the p value and a significance level assumed \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is higher than 210250 at 5% of significance.  

You might be interested in
Change to a percent rounded to the nearest hundredth of a percent if necessary. 1 1/4, 3/5, 5/8, 1/3, 2/7
Gelneren [198K]

Answer:

1.3%,60%,33%,.3% is this right

4 0
3 years ago
Identify the parent function name and equation​
Andreas93 [3]
Their is nothing for us to answer.
7 0
3 years ago
Jessica walks 7 times as far to school as Taylor does . Jessica walks 5 miles. How many miles does Taylor walk?
Kaylis [27]

Answer:

Step-by-step explanation:

Jessica: 5 miles

Taylor: 5/7 = .7143 miles

3 0
3 years ago
Jen buys 4 tires for 272$
Nostrana [21]
What are you asking if all together they are 272 then each tire would cost 68 dollars
8 0
3 years ago
Combine like terms. 3y-4-6-3x-7y+6x+1
maks197457 [2]

Answer:

If you combine everything its <em>-4y+3x-9</em>

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Please help me with this thanks :)
    10·1 answer
  • Find the solutions to the system
    13·1 answer
  • A building contractor has a piece of crown molding that is 48 ½ inches long. He cuts off one piece measuring 10 ¼ inches and ano
    14·1 answer
  • Find the value of z.
    13·1 answer
  • Joanna created a rectangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a ba
    9·1 answer
  • Daniel combines 6.42 liters of red paint with 6.87 liters of blue paint to make purple paint. He pours the paint equally into 3
    5·1 answer
  • Please solve this will mark brainliest and follow -Thanks
    8·1 answer
  • Select the correct answer. Each of the four angles of a quadrilateral measures 90°. How many rectangles can you construct using
    11·2 answers
  • What fraction best represents 5x2/3
    6·1 answer
  • Jenny, Keith, and Joanna participated in a mini-
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!