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
Paul [167]
2 years ago
10

A manufacturer of precision measuring instruments claims that the standarddeviation in the use of the instruments is less than 0

.00002 millimeter. An analyst,who is unaware of claim, uses the instrument eight times and obtains a samplestandard deviation of 0.00001 millimeter. Assume normal population(i) Confirm using a test procedure and α level of 0.01 that there is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.(ii) Find the P-value for this test? How does it compare with α(greater than or less than)? Does it make sense with respect to your conclusionin part (i)?
Mathematics
1 answer:
alexdok [17]2 years ago
7 0

Answer:

i) There is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.

ii) p_v= P(\chi^2_{7}

Step-by-step explanation:

s=0.00001 represent the sample standard deviation

\alpha =0.01 represent the significance level for the test

\sigma_o =0.00002 represent the value that we want to test

n=8 represent the sample size

A chi-square test can be used to test "if the standard deviation of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test".

Null and alternatve hypothesis

The system of hypothesis on this case would be given by:

Null Hypothesis: \sigma \geq 0.00002

Alternative Hypothesis: \sigma

The statistic to test this is given by:

T=(n-1)(\frac{s}{\sigma_0})^2   (1)

Part i) Calculate the statistic

If we replace into formula (1) we got this:

T=(8-1)(\frac{0.00001}{0.00002})^2 =1.75   (1)

The critical region for a for a lower one-tailed alternative is given by

T< \chi^2_{1-\alpha/2,N-1}

The degrees of freedom are given by

df=n-1=8-1=7

And if we use the Chi Square distribution with 7 degrees of freedom we see that \chi^2_{1-0.01/2,7}=1.239

And our critical region would be T< 1.239 so on this case we can conclude that we fail to reject the null hypothesis. So it's not enough evidence to conclude that the population standard deviation is less than 0.00002 mm.

Part ii) Calculate the p value

In order to calculate the p value we can do this:

p_v= P(\chi^2_{7}

If we compare this value with the significance level (0.01) we see that p_v>\alpha

This agrees with the conclusion since when the p values is greater than the significance level we FAIL to reject the null hypothesis, same conclusion as part i).

You might be interested in
HELP I GIVE BRAINS TO RIGHT ANSWER
Aneli [31]
4 + (2)^4
4 + 16 = 20
5 0
2 years ago
Who plays forza horizon 3
Butoxors [25]

Answer:

I recently got it on my xbox

Step-by-step explanation:

I usually play with the family my name on xbox is wood  

8 0
2 years ago
Read 2 more answers
Pat sewed 200 tote bags in 4 hours at what rate did pat sew the tote bags
Alik [6]

Answer:

50 tote bags were sewed per hour

Step-by-step explanation:


6 0
3 years ago
A falcon flies 300 kilometers per hour. A goose flies 140 kilometers per hour. If a falcon and a goose each fly for 2 hours, how
Mila [183]

Answer:

320

Step-by-step explanation:

Distance covered by falcon in 2 hours=300*2=600 km

Distance covered by goose in 2 hours=140*2=280 km.

Falcon flew 600-280=320 km more than goose

7 0
3 years ago
Find angle measures and arc measures
Vlad1618 [11]

Answer:

Step-by-step explanation:

a. We know that KH is a diameter of the circle and that along angles along it on either side adds up to 180° as it's a straight line.

-Therefore, we have that:

m\angle a+ \angle GaH=180\textdegree\\\\\\m\angle a=180-35\\\\=145\textdegree

Hence, the angle a is equal to 180°

b.We know that GJ is a diameter of the circle and that along angles along it on either side adds up to 180° as it's a straight line.

-Therefore, we have that:

m\angle b+\angle GaK=180\textdegree\\\\m\angle b=180\textdegree -145\textdegree\\\\\\\\=35\textdegree

Hence, the angle b is equal to 35°

3 0
3 years ago
Other questions:
  • Solve the system of equations.<br> 12x-5y=-20<br> y=x+4
    9·1 answer
  • Helpppppppppppppppp meeeee asap
    8·1 answer
  • For homework Sarah had seventeen math problems and twenty-eight spelling problems. If she can finish five problems in an hour ho
    12·1 answer
  • use your knowledge of angle relationships solve for x in the diagram below Justify Your solution by naming the geometric relatio
    14·1 answer
  • 1
    6·1 answer
  • Evaluate: (x^2-1)/(x-1) if x goes to 1?
    11·1 answer
  • Someone please help me, this test determines if I pass or not.
    10·1 answer
  • Mr Jones bought a snowboard. The 6% sales tax on the snowboard was $32.50. What was the total cost including the sales tax? (rou
    13·1 answer
  • 177 ×44 Please hurry but take your time​
    12·2 answers
  • Help me to solve this question
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!