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
Nesterboy [21]
3 years ago
10

A professor at a university wants to estimate the average number of hours of sleep students get during exam week. The professor

wants to find a sample mean that is within 1.939 hours of the true average for all college students at the university with 90% confidence. If the professor knows the standard deviation of the sleep times for all college students is 6.995, what sample size will need to be taken
Mathematics
1 answer:
kotegsom [21]3 years ago
4 0

Answer:

n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36

So the answer for this case would be n=36 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma =6.995 represent the population standard deviation

n represent the sample size  

Solution to the problem

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =1.939 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

If we replace we have this:

n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36

So the answer for this case would be n=36 rounded up to the nearest integer

You might be interested in
Noah and his children went into a grocery store and where they sell apples for $1
Black_prince [1.1K]

Answer:

8

Step-by-step explanation:

Since Noah has decided to buy 4 apples, that means he has decided to spend $4 on apples. Deducting that from $20, you are left with $16. Divide this total by the cost of each mango, $2, and you get the result as 8 mangos.

4 0
3 years ago
ΔDEF is similar to ΔABC as shown below, and x represents the length of segment EF.
Marysya12 [62]
Explaining- when you look at the vertex to the other vertex you see the length and that is when you multiply

Answer- A
4 0
2 years ago
Help me with this!! I will mark Brainliest ❤️
soldi70 [24.7K]
28 because it is qhal
5 0
2 years ago
The sum of two numbers is 72. One number is 8
Tpy6a [65]

Answer:

32 and 40

Step-by-step explanation:

Let's call the smaller number x. If the smaller number is x, the equation for this problem is 2x + 8 = 72

Equation:

2x + 8 = 72

2x = 64

x = 32

So now we know the smaller number is 32, so now add 8 and we get 40.

Therefore the 2 numbers are 32 and 40

7 0
3 years ago
Brenna owns 9 T-shirts, 3 of which are red.
Ulleksa [173]

Answer:

1/3

Step-by-step explanation:

9 Shirts, 3 are Red

Probability: 3/9

Simplify: 1/3

5 0
3 years ago
Other questions:
  • I have no idea what im doing someone help pls! due soon
    6·2 answers
  • a similar figure compared to the original figure is ___ a translation. A.) sometimes B.) never C.) always D.) none of these choi
    10·1 answer
  • What is the answer for 5.2 × 10-9 + 3.1 × 10-8 = × 10?
    13·1 answer
  • Give the slope and y-intercept of the line whose equation is y = -6x + 7
    7·1 answer
  • 30 POINTS: There are 80 seats on a train. 25% of the seats are empty. How many empty seats are there on the train?
    14·2 answers
  • What is the discount on a leather jacket that costs $298 discounted at 15%
    8·2 answers
  • Based on the diagram, what is sin A<br> Enter your answer in the boxes.<br> sin A =
    14·1 answer
  • Which equation is in slop-intercept form?
    15·2 answers
  • Simply the expression below <br><br> (10-3i)(2-5i)
    14·2 answers
  • Find X please I really need help. Explain the best you can! Thanks!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!