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
wolverine [178]
3 years ago
9

The manufacturer of hardness testing equipment uses​ steel-ball indenters to penetrate metal that is being tested.​ However, the

manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of​ indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.​ Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a​ 95% confidence interval to judge whether the two indenters result in different measurements.
Mathematics
1 answer:
kumpel [21]3 years ago
3 0

Answer:

Check the explanation

Step-by-step explanation:

Let X denotes steel ball and Y denotes diamond

\bar{x_1} = 1/9( 50+57+......+51+53)

=530/9

=58.89

\bar{x_2}= 1/9( 52+ 56+....+ 51+ 56)

=543/9

=60.33

difference = d =(60.33- 58.89)

=1.44

s^2=1/n\sum xi^2 - n/(n-1)\bar{x}^2

s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2

=31686/8 - 9/8( 3468.03)

=3960.75 - 3901.53

=59.22

s1 = 7.69

s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2

=33295/8 - 9/8 (3640.11)

=4161.875 - 4095.12

=66.75

s2 =8.17

sample standard deviation for difference is

s=\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}

 = \sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}

= \sqrt{1007.76/16}

=7.93

sd = s*\sqrt{(1/n1)+(1/n2)}

=7.93*\sqrt{(1/9)+(1/9)}

=7.93* 0.47

=3.74

For 95% confidence level Z (\alpha /2) =1.96

confidence interval is

d\pm Z(\alpha /2)*s_d

=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)

=(1.44 - 7.35 , 1.44 + 7.35)

=(-2.31, 8.79)

There is sufficient evidence to conclude that the two indenters produce different hardness readings.

You might be interested in
3. PENTAGON The Pentagon is a five-sided
Sergeu [11.5K]
The answer is 4605 feet since 921 • 5 is 4605. There are 5 sides and each side 921 so 921 • 5 = 4605 would be the answer
5 0
3 years ago
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste
olga_2 [115]
1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.

2. So f(x)=(x-a)^{3}

3. Don't forget that the expression might have a coefficient b as well, and still maintain the conditions: 
 
f(x)=b(x-a)^{3}

4. Now, f(0)=-5 so  -5=f(0)=b(0-a)^{3}=b(-a) ^{3}=-ba ^{3}

-5=-ba ^{3}

5=ba ^{3}

b= \frac{5}{ a^{3} }

5. the function is f(x)=\frac{5}{ a^{3} }(x-a)^{3} where a can be any real number except 0
7 0
3 years ago
Read 2 more answers
Help asap pleeeas!
olga_2 [115]
The answer to this question is C.2 I think
6 0
2 years ago
Read 2 more answers
Find The Value Of x ?
slega [8]

<u>Answer</u>:

1) x  = -1  ||     2) x = 10

<u>Explanation</u>:

1)

→ \log _3\left(\frac{1}{3}\right)=x

→ \frac{1}{3}  = 3^x

→ 3^{-1} = 3^x

→ x  = -1

2)

→ \log _3\left(x-1\right)=2

→ x - 1 = 3^2

→ x -1 = 9

→ x = 9 +1

→ x = 10

5 0
2 years ago
Read 2 more answers
Jessica can build a bookshelf in 4 hours. Sydney can build a bookshelf in 6 hr. How long will it take them if they build the boo
Dominik [7]

Answer:

2 hours

Step-by-step explanation:

i think

4 0
3 years ago
Read 2 more answers
Other questions:
  • How many 2 litre glasses of water are in a 3.6 litre pitcher
    12·1 answer
  • 1. Solve for x.<br><br> Need help in math
    5·1 answer
  • what is the probability that a randomly selected person will be in a traffic accident and be on their cell phone?
    6·1 answer
  • Jason drove 4/5 of the way to his destination if he drove 480 miles what is his total distance of his trip
    8·1 answer
  • Kay is drawing a triangle. Two of the sides have an equal length of 8 cm, and the angle between those sides measures 68°. Which
    13·1 answer
  • I can’t figure out how to use the zeros in the polynomial. Please explain
    12·1 answer
  • Irene made a mistake when she solved this inequality:
    7·1 answer
  • Write an inequality , the sum of a number and 4 is less than 6
    12·1 answer
  • 2x + y = −3<br> 3x + 2y = −8
    8·1 answer
  • On Saturday evening, you bowl at Mar Vista Bowling where renting shoes costs $2 and each game bowled is $3.50. On Sunday night,
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!