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
ehidna [41]
3 years ago
14

Suppose that at a state college, a random sample of 41 students is drawn, and each of the 41 students in the sample is asked to

measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this college turns out to be (21.709, 25.091). If instead a 90% confidence interval was calculated, how would it differ from the 95% confidence interval?
Mathematics
1 answer:
ra1l [238]3 years ago
3 0

Answer:

The  confidence interval for 90% confidence would be narrower than the 95% confidence

Step-by-step explanation:

From the question we are told that

  The  sample size is n = 41

   

For a 95% confidence the level of significance is  \alpha  = [100 - 95]\% =  0.05 and

the critical value  of  \frac{\alpha }{2}  is   Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }=  1.96

For a 90% confidence the level of significance is  \alpha  = [100 - 90]\% =  0.10 and

the critical value  of  \frac{\alpha }{2}  is   Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} }=  1.645

So we see with decreasing confidence level the critical value  decrease

Now the margin of error is mathematically represented as

         E =  Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }

given that other values are constant and only Z_{\frac{\alpha }{2} } is varying we have that

         E\ \  \alpha \ \   Z_{\frac{\alpha }{2} }

Hence for  reducing confidence level the margin of error will be reducing

  The  confidence interval is mathematically represented as

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

Now looking at the above formula and information that we have deduced so far we can infer that as the confidence level reduces , the critical value  reduces, the margin of error  reduces and the confidence interval becomes narrower

You might be interested in
Amy works for 36 hours per week for 10 weeks during the summer, making $\$3000$. If she works for 30 weeks during the school yea
Zinaida [17]

Answer:

12 hours per week

Step-by-step explanation:

1. Find how many hours she worked to make $3,000 (36x10=360 hours)

2. divide 360 hours by 30 weeks

she would need to work 12 hours per week to make $3,000

6 0
3 years ago
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse
Drupady [299]

Answer:

a'(d) = \frac{d}{5} + \frac{3}{5}

a(a'(d)) = a'(a(d)) = d

Step-by-step explanation:

Given

a(d) = 5d - 3

Solving (a): Write as inverse function

a(d) = 5d - 3

Represent a(d) as y

y = 5d - 3

Swap positions of d and y

d = 5y - 3

Make y the subject

5y = d + 3

y = \frac{d}{5} + \frac{3}{5}

Replace y with a'(d)

a'(d) = \frac{d}{5} + \frac{3}{5}

Prove that a(d) and a'(d) are inverse functions

a'(d) = \frac{d}{5} + \frac{3}{5} and a(d) = 5d - 3

To do this, we prove that:

a(a'(d)) = a'(a(d)) = d

Solving for a(a'(d))

a(a'(d))  = a(\frac{d}{5} + \frac{3}{5})

Substitute \frac{d}{5} + \frac{3}{5} for d in  a(d) = 5d - 3

a(a'(d))  = 5(\frac{d}{5} + \frac{3}{5}) - 3

a(a'(d))  = \frac{5d}{5} + \frac{15}{5} - 3

a(a'(d))  = d + 3 - 3

a(a'(d))  = d

Solving for: a'(a(d))

a'(a(d)) = a'(5d - 3)

Substitute 5d - 3 for d in a'(d) = \frac{d}{5} + \frac{3}{5}

a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}

Add fractions

a'(a(d)) = \frac{5d - 3+3}{5}

a'(a(d)) = \frac{5d}{5}

a'(a(d)) = d

Hence:

a(a'(d)) = a'(a(d)) = d

7 0
2 years ago
If there are 680 calories in 8 oz of ground beef, how many
irina [24]

Answer:

3/8ths of 680 kcal or 3 x 85 = 255 kcal.

Step-by-step explanation:

3/8ths of 680 kcal or 3 x 85 = 255 kcal.

6 0
2 years ago
Read 2 more answers
A right triangle with two congruent legs is always a 45-45-90 triangle.
saw5 [17]

Answer:

True

Step-by-step explanation:

I think this is a true or false question and this is a true statement.

6 0
3 years ago
Read 2 more answers
HELP PLEASE BE QUICK
In-s [12.5K]

Answer: it equals 20

Step-by-step explanation:

10 x 20 = 120, hoped this helped.

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the probability that a randomly selected person surveyed has a job, given that the person is less than 18 years old? Exp
    7·2 answers
  • Fill in the bubble next to the correct answer
    13·2 answers
  • Suppose x and y are related by the given equation and use implicit differentiation to determine dydx.x7y+y7x=7.
    10·1 answer
  • Which letter has at least one line of symmetry? <br> a.D<br> b.J<br> c.G<br> d.L
    5·1 answer
  • State if the triangles in each pair are similar. If so, state how they are similar and complete the similarity statement​.
    5·1 answer
  • How many solutions exist for the system of equations graphed below?
    14·2 answers
  • I WILL MARK BRAINIEST
    12·2 answers
  • The two triangles below are congruent. Which of the following are congruent by CPCTC?
    15·2 answers
  • I need help pleaseee):
    8·1 answer
  • Need help with 3 pls that’s all
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!