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
saw5 [17]
3 years ago
5

The data below were obtained from an experiment were participants were given drinks with or without caffeine and then asked to t

ap their fingers. The data for 20 participants are below. Assume the number of taps per minute is normally distributed. The variance is unknown. Find a 95% CI for μ number of taps. Identify the pivot function used. 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
8 0

Answer:

The  95% confidence interval is  244.26  <  \mu < 246.95  

The pivot function used is  

           t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }

Step-by-step explanation:

From the question we are told that

  The  data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242

  The  sample  size is  n=  20

   

Given that the confidence level is 95% then the level of significance is

      \alpha = (100 - 95)\%

      \alpha =  0.05

The  degree of freedom is mathematically represented as

    df =  20 -1

    df =  19

From the student t-distribution table  the critical value of  \frac{\alpha }{2}  is  

          t_{\frac{\alpha }{2} ,  19 } =  2.093

The mean is mathematically represented as

          \= x  = \frac{\sum x_i}{ n}

         \= x  = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}\= x  =  246.6

The standard deviation is mathematically represented as

            \sigma  = \sqrt{\frac{\sum (x_i -  \= x )^2)}{n} }

           \sigma  = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..

             \ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...

              \ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+  (242-246.6)^2+  (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...       \sqrt{\frac{ (245-246.6)^2+  (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }\sigma =  2.87411

The margin of error is mathematically represented as

       E =  t_{\frac{\alpha }{2} , 19} *  \frac{\sigma }{\sqrt{n} }

      E =  2.093 *  \frac{2.87411 }{\sqrt{20} }

      E =  1.345

The 95% confidence interval is mathematically represented as

       \= x  -  E  <  \mu < \= x  +  E

=>   245.6 - 1.345  <  \mu

=>    244.26  <  \mu < 246.95  

The pivot function used is  

           t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }

     

You might be interested in
2/7 • 9 1/10<br> Please help
nordsb [41]
\frac{2}{7} * 9 \frac{1}{10} =  \frac{2}{7} *  \frac{91}{10} =  \frac{2~*~91}{7~*~10} =  \frac{182}{70} = 2 \frac{42}{70} = 2  \frac{3}{5}
3 0
2 years ago
Read 2 more answers
an angles measure is 6 degrees more than 3 times the measure of its complwment. find the measure of the angles.
irina1246 [14]

Answer:

The angles are 22.5 and 67.5.

Step-by-step explanation:

A complement is the angle that when added to the given angle gives 90 degrees.

Therefore, the angle x is 3 times larger than its complement.

This means that x is 3/4 of 90 degrees and complement is 1/4 of 90 degrees.

Therefore, the angles are 22.5 and 67.5.

3 0
2 years ago
The vertices of a hyperbola are located at (−4, 1) and (4, 1). The foci of the same hyperbola are located at (−5, 1) and (5, 1).
topjm [15]

Answer:

x^2\ 16 - y^2/9 = 1

step-by-step explanation:

soooo the equation for a hyperbola that is horizontal is x^2/a^2 - y^2/b^2 = 1

a hyperbola should always equal one so dont forget that when writing your equation becuase it is easy to forget.

it helps to graph this so you can see it better

to find a it is the distance from the center to the vertices which is 4 so in the equation you will write 16 becuase it is a^2

then you need to find b. to get b you have to figure out that c is the distance from the center to the foci which is 5 and it is all related to the plythagorm theorum becuase it forms a right triangle. so you do c^2 - a^2 = b^2

you get 9 for b^2 because 25-16=9 and so you put that in the equation

3 0
3 years ago
Read 2 more answers
Always ? Sometimes? Never <br> Explain
Stels [109]

Answer:

Sometimes

Step-by-step explanation:

Quadrilaterals are shapes with four sides.

This means some quadrilaterals will have 4 equal sides, others will have <em>no </em>equal sides!

There is no rule determining side length equivalence in quadrilaterals. But those may be sub-classified as other shapes.

6 0
2 years ago
The moon is about 240000 miles from earth.What is the distance written as a whole number multiplied by a power of ten
Sauron [17]
A whole number? ok. 24x10^4. usually though you would use standard form so it would be 2.4x10^5
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the answer to 90x144?
    9·1 answer
  • Find the sum of the three expressions and choose the correct answer. -8a 3 b + 3a2 b 2 - 5 2 + 5a 2 b 2 3a 3 b + 7 - 9a 2 b 2
    15·1 answer
  • What is the total surace area of the cylinder? Write your answer as a polynomial in standard form.
    6·2 answers
  • The volume of a cube is 400 m3. Which statements are true about the same cube measured in cubic centimeters? Choose all answers
    12·1 answer
  • PLEASE HELP, I NEED THE ANSWERS ASAP, I WILL AWARD BRAINLIEST!
    9·1 answer
  • Use the table to determine whether the relationship is proportional. If so, write an equation for the relationship. Tell what ea
    11·1 answer
  • Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Lou​'s car had 5.3
    6·1 answer
  • If S.P = rs 6200 and C.P = rs 6400 find profit or loss plzzzz tell me answer I will make brainlist​
    10·2 answers
  • Please help meeeeeee​
    14·2 answers
  • The following table gives the statements and justifications for solving the equation 4(x - 7) + 14 =
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!