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]
2 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]2 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
in your class 7 students do not receive weekly allowance, 5 students receive $3, 7 students receive $5, 3 students receive $6, a
Gemiola [76]
The mean is the average of a set of numbers.
To find the mean of this data, form a number set by gathering all the numbers.
We need to find the average weekly allowance. To do this, each number in the number set should be the different allowances, and their quantity is the number of students who earned that allowance.
In this case, there would be seven 0s, five 3s, seven 5s, three 6s, and two 8s.

The numbers are:
0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 8, 8

To find the mean of these numbers, add then together then divide by the total amount of numbers.

This means doing:
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 3 + 3 + 3 + 3 + 3 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 8 + 8) / 7 + 5 + 7 + 3 + 2

An easier formula could be used by using multiplication.
This would be [7(0) + 5(3) + 7(5) + 3(6) + 2(8)] / 24
This is a lot easier to read!
Now to solve it.
7 • 0 = 0
5 • 3 = 15
7 • 5 = 35
3 • 6 = 18
2 • 8 = 16
0 + 15 + 35 + 18 + 16 = 84
84 / 24 = 3.5

The mean is 3.5, or $3.50
This means that the average weekly allowance amongst these students is $3.50.

Hope this helps!
4 0
3 years ago
PLEASE SOLVE!!!! ASAP!!!! Thanks<br><br> 2[(∛8)²+1/8*16]
ehidna [41]
2[(∛8)²+1/8*16]

(∛8)² = (∛8) x (∛8) = (∛64) = 4
1/8 *16 = 16/8 = 2
Total expression = 2 * (4+2)= 12

6 0
3 years ago
A line through which two points would be parallel to a line with a slope of 3/4?
Mumz [18]

Answer:

F. (0, 5) and (-4, 2)

Step-by-step explanation:

We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:

F. (0,5) and (-4,2) As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4. This is the line with slope 3/4.

5 0
3 years ago
Describe five ways to represent a function ?
Over [174]
1. A function can be represented verbally. For example, the circumference of a square is four times one of its sides.

2. A function can be represented algebraically. For example, 3x+6 3 x + 6.

3.A function can be represented numerically.

4. A function can be represented graphically.

I only found four, hopefully this helps.
6 0
3 years ago
HELP ME WITH MY MATH EXAM FAST
Ostrovityanka [42]

Answer:

sorry can't help :)

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • There are 7 boys in a class of 15 students ( a ) what is the ratioo of all students in the class to girls? (b) what is the ratio
    6·1 answer
  • 50% of all the cakes Jenny baked that week were party cakes,
    6·1 answer
  • Write the prime factorization of 90. Use exponents where possible.
    13·1 answer
  • What 3+3+3+3+3-2????
    15·2 answers
  • what is the volume of a cylinder, in cubic cm, with a height of 19cm an a base diameter of 6cm? round to the nearest tenths plac
    8·2 answers
  • Dialiting a triangle changes the angles and side length of the triangle true or false
    13·1 answer
  • For what value(s) of k will the relation not be a function
    10·1 answer
  • Convert the number to scientific notation. 0.000001019<br>​
    9·2 answers
  • Consider the example below. Explain in your own words why the equation is wrong. (4^-2)^2=1/16
    11·1 answer
  • Help me with this exam explanations only
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!