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
vovangra [49]
2 years ago
9

Find the 95% confidence interval for estimating the population mean μ

Mathematics
1 answer:
AVprozaik [17]2 years ago
8 0

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

  • \displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}

We are given these variables:

  • \overline{x}=50
  • n=60
  • \sigma=10

Plug these values into the formula for the confidence interval:

  • \displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

  • \displaystyle \frac{1-C}{2}=A

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

  • \displaystyle \frac{1-.95}{2}=.025

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

  • t^*=1.96

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

  • \displaystyle 50\pm 1.96 \big{(}\frac{10}{\sqrt{60} } \big{)}

We can calculate the confidence interval, using this formula, to be:

  • \boxed{(47.4697, \ 52.5303)}

<h3>Interpreting the Confidence Interval</h3>

We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

You might be interested in
Once again Bri needs help so ya btw make it a step-by-step please
Masja [62]

Answer:

the fourth clock listed option D?

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
A strobe light is located at the center of a square dance room. the rotating light is 40 feet from each of the square walls and
Effectus [21]

The equation of the rotating light is an illustration of a secant function

The equation that represents the distance between the center of the circle and the light source is d(t) = 40\sec(\frac{\pi}{3}t)

<h3>How to determine the equation</h3>

The equation is a secant function represented by

y =A\sec(Bt)

Where:

A represents the amplitude

So, we have:

A = 40 --- the distance of the light from each square wall

B represents the period, and it is calculated as:

B = \frac{2\pi}{T}

The light completes its full rotation every 6 seconds.

This means that,

T = 6

So, we have:

B = \frac{2\pi}{6}

Simplify

B = \frac{\pi}{3}

Substitute values for A and B in y =A\sec(Bt)

y = 40\sec(\frac{\pi}{3}t)

Rewrite as a function

d(t) = 40\sec(\frac{\pi}{3}t)

Hence, the equation that represents the distance between the center of the circle and the light source is d(t) = 40\sec(\frac{\pi}{3}t)

Read more about trigonometry functions at:

brainly.com/question/1143565

5 0
2 years ago
WILL BE GIVING BRAINLIEST, 5 STARS, AND THANKS WITHIN AN HOUR.
pantera1 [17]
39.5 i am pretty suree of it :P
4 0
3 years ago
The square of a number is 3 less than four times the number. Which values could be the number? 0 0 -3 O 1​
grigory [225]

Answer:

3 and/or 1.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the answer to 10-(8p+3)=9(2p-5) ?
aniked [119]

Use distribution.
10 - (8p + 3) = 10 - 8p - 3 = 7 - 8p
9(2p - 5) = 18p - 45

So...
-8p + 7 = 18p - 45
Subtract 7 from both sides
-8p = 18p - 52
Subtract 18p from both sides
-26p = 52
Divide both sides by -26.
p = -2

There's your answer :D

6 0
4 years ago
Read 2 more answers
Other questions:
  • 7 divided by 2 = 7/2
    14·1 answer
  • Which of the following functions gives the length of the base edge, a(v), of a right square pyramid that is 8 inches tall as a f
    11·1 answer
  • 28. The United States Postal Service delivers many packages every day. A postal carrier recorded the number of packages he deliv
    14·2 answers
  • Civil engineer wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He ass
    10·1 answer
  • li needs 15 pieces of string each 1/2 of a inch long. she cut a 6-inch piece of string into pieces that are 1/2 of an inch long
    12·2 answers
  • Un bloque de 65 kg en un plano horizontal, es empujado por una fuerza de 380 N a un ángulo de 15° respecto a la horizontal. Si e
    8·1 answer
  • If a certain roundabout has diameter of 96 feet,
    13·1 answer
  • PLEASE PLEASE PLEASE HELP I WIL GIVE BRAINLIEST<br> ALSO PLS SHOW WORK
    6·2 answers
  • Find the value of x using trig please .....
    6·1 answer
  • The diagram below shows 4-sided shape categories that flow from one to another.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!