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
Y_Kistochka [10]
3 years ago
6

In estimating the mean score on a fitness exam, we use an original sample of size and a bootstrap distribution containing bootst

rap samples to obtain a confidence interval of to . A change in this process is described below. If all else stays the same, which of the following confidence intervals (A, B, or C) is the most likely result after the change: Using an original sample of size n 16?
A. 66 to 74
B. 67 to 73
C. 67.5 to 72.5
Mathematics
1 answer:
zmey [24]3 years ago
3 0

Answer:

Option A is correct.

The confidence interval becomes

66 to 74.

Step-by-step explanation:

Complete Correct Question

In estimating the mean score on a fitness exam, we use an original sample of size n = 30 and a bootstrap distribution containing 5000 bootstrap samples to obtain a 95% confidence interval of 67 to 73. A change in this process is described below. If all else stays the same, which of the following confidence intervals (A, B, or C) is the most likely result after the change: Using an original sample of size n=16?A. 66 to 74

B. 67 to 73

C. 67.5 to 72.

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

To calculate the Sample Mean, we will use the confidence imterval obtained for the first sample size of 30 was 67 to 73.

Let the mean be x and the margin of error = y.

Lower limit of the confidence interval = x - y = 67

Upper limit of the confidence interval = x + y = 73

Solving simultaneously,

Sample mean = 70

Margin of error = 3

Then, since the sample size was initially 30, the critical value was obtained from the z-tables.

95% critical value = z = 1.960

Margin of error = (critical value) × (standard error)

3 = 1.960 × (standard error)

Standard error = 1.5306

Standard error of the mean = σₓ = (σ/√n) = 1.5306

σ = standard deviation of the sample = ?

n = sample size = 30

1.5306 = (σ/√30)

σ = 1.5306 × √30 = 8.3835

Note that using the central limit theorem, we can assume that sample mean for a sample size of 30 people will be approximately equal to the same value, digital value, that is Adam score of 70.

Sample mean for sample size 16, = 70

Sample standard deviation = 8.3835

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

Critical value = 1.960

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 8.3835

n = sample size = 16

σₓ = (8.3835/√16) = 2.096

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 70 ± (1.960 × 2.096)

CI = 70 ± 4.10

95% CI = (65.9, 74.1)

95% Confidence interval = (66, 74)

Hope this Helps!!!

You might be interested in
QN (b) plz solve it fast ​
Alex17521 [72]

Answer:

Look I dont know the answer.

Step-by-step explanation:

but look their is an aapp called MATH installed it and w you will get the answer

4 0
3 years ago
Find the slope of the line that passes through (6, 1) and (8, 2)
Aleksandr [31]

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em><em> </em><em>⤴</em>

<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>:</em><em>)</em>

7 0
3 years ago
Read 2 more answers
Which point is an x-intercept of the quadratic function f(x)=(x-4)(x+2)
Mademuasel [1]

Answer:

x = - 2 or x = 4

Step-by-step explanation:

To find the x- intercepts let f(x) = 0, that is

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

The x- intercepts are at x = - 2, x = 4

3 0
2 years ago
Match each equation with the number that makes it true.
Burka [1]
Number 1 is 15 number 2 is 9x3=27 and number 3 is 15 and number 4 is 5x7=35 number number 6 is 5 number 7 is 11 and that is about all i know hope this helps
3 0
3 years ago
Read 2 more answers
What percent do you actually pay if 40% discount
Yanka [14]

Answer:

60%

Step-by-step explanation:

A 40% discount means that 40% will be off, meaning you won't have to pay 40% of the original price. Therefore, you only pay 60% of the original price (100% - 40% = 60%).

4 0
3 years ago
Other questions:
  • An analyst is creating a graph to show the salaries
    7·2 answers
  • What is the following sum? 4 sqrt 5 + 2 sqrt 5
    10·2 answers
  • What is the equivalent ratio for 19:7?
    12·1 answer
  • Which statement about the quadratic parent function is true?
    13·2 answers
  • Solve 4x^5-12x^4+x^3-52x^2-60x-16=0
    11·1 answer
  • 15 pts!!!! plzzzz Help When U read this!!!!!or else!!!!!Consider the following equation.
    8·1 answer
  • You want to open a checking account at your local bank which offers two options. A standard checking account charges $6 each mon
    13·1 answer
  • What does x equal?<br><br> 3/4 times x + 7 = -5
    13·1 answer
  • Can someone help me??
    12·1 answer
  • Help me with this math question please
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!