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
user100 [1]
3 years ago
7

The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.

A random sample of 15 devices is selected and found to have an average life of 5311.4 hours and a sample standard deviation of 220.7 hours.
a. Test the hypothesis that the true mean life of a biomedical device is greater than 500 using the P-value approach.
b. Construct a 95% lower confidence bound on the mean.
c. Use the confidence bound found in part (b) to test the hypothesis.
Mathematics
1 answer:
tatuchka [14]3 years ago
5 0

Answer:

a)Null hypothesis:- H₀: μ> 500

  Alternative hypothesis:-H₁ : μ< 500

b) (5211.05 , 5411.7)

95% lower confidence bound on the mean.

c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Step-by-step explanation:

<u>Step :-1</u>

Given  a random sample of 15 devices is selected in the laboratory.

size of the small sample 'n' = 15

An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.

Average of sample mean (x⁻) =  5311.4 hours

sample standard deviation (S) = 220.7 hours.

<u>Step :- 2</u>

<u>a) Null hypothesis</u>:- H₀: μ> 500

<u>Alternative hypothesis</u>:-H₁ : μ< 500

<u>Level of significance</u> :- α = 0.95 or 0.05

b) The test statistic

t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }

t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }

t = 5.826

The degrees of freedom γ= n-1 = 15-1 =14

tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.

Null hypothesis is rejected at  95% confidence on the mean.

C) <u>The 95% of confidence limits </u>

(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )

substitute values and simplification , we get

(5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )

(5211.05 , 5411.7)

95% lower confidence bound on the mean.

You might be interested in
What is the surface area of the cylinder d = 10 h = 7
Anna11 [10]
The answer is 120\pi. Hope I helped!
3 0
3 years ago
Anyone want to help me with math
Xelga [282]

Ok, I am ready, what are the questions.

Tell me in the comment section

6 0
3 years ago
Which expression is equivalent to 3/2*3/2*3/2*3/2
lesantik [10]

Answer:

hello :

(3/2)×(3/2)×(3/2)×(3/2) = (3/2)^4


8 0
3 years ago
Which of the following fractions have repeating decimal representations? Which have terminating decimal representations?
natali 33 [55]

Repeating decimal representation will be 3/13, 7/24. Terminating decimal representation will be 3/16, 4/125.

<h3>What is decimal?</h3>

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The base-10 number system, arguably the most widely used number system, is referred to as decimal. The decimal number system consists of ten single-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The number following nine is 10.

Here,

Repeating decimal representation,

=3/13, 7/24

Terminating decimal representation,

=3/16, 4/125

3/13 and 7/24 will be repeated in decimal form. The final two decimal places are 3/16 and 4/125.

To know more about decimal,

brainly.com/question/25903211

#SPJ1

7 0
1 year ago
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
amm1812

Answer:

The solution of this system of equations is (3 , -8)

Step-by-step explanation:

The given system is

x + 2y = -13

12x + 5y = -4

We make x the subject of the first equation and put it into the second:

x =  - 13 - 2y

We put this expression for x into the second equation

12(-13-2y)+5y=-4

-156-24y+5y=-4

-24y+5y=-4+156

-19y=152

y=-8

We substitute y=-8 into x=-13-2y to get:

x =  - 13 - 2( - 8) = 3

The solution of this system of equations is (3 , -8)

3 0
3 years ago
Other questions:
  • Can people please help me on this
    6·1 answer
  • on a trip from Virginia to Florida the Sampson family wants to travel at least 420 miles in 8 hours of driving. what must be the
    6·2 answers
  • a museum opened at 8:00 am. in the first hour 350 people purchased admission tickets. in the 2nd hour 20% more people purchased
    8·1 answer
  • Please Help me! 20 pts. n i will mark you as brainliest!
    9·2 answers
  • A2 + 100= 144 what is a
    14·1 answer
  • The midpoint of AB is (-4,-7) if the coordinates of A are (-7,-6) what are the coordinates of B
    12·1 answer
  •   Classify the system and determine the number of solutions. Check all that apply. {7x + y = 13 28x + 4y = -12 A) inconsistent B
    14·1 answer
  • Circle O has a circumference of 367 cm.
    13·1 answer
  • OMG PLZ HELP I NEED THIS NOW!!
    10·1 answer
  • PLEASE HELP AS SOON AS POSSIBLE
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!