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
meriva
2 years ago
10

In order to ensure efficient usage of a server, it is necessary to estimate the mean number

Mathematics
1 answer:
juin [17]2 years ago
7 0

Answer:

a. [36.19;39.21]

b. Reject the null hypothesis. The population mean of users that are connected at the same time is greater than 35.

Step-by-step explanation:

Hello!

Your study variable is,

X: "number of users of one server at a time"

The objective is to estimate the mean, for this, a sample of n=100 times was taken and the standard deviation S= 9.2 and the sample mean is X[bar]= 37.7 were calculated.

You need to study the population mean, for this you need your variable to have at least normal distribution. Since you don't have information about its distribution, but the sample is big enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean X[bar] to normal:

X[bar]≈N(μ;σ²/n)

a. With this approximation, you can construct the 90% Confidence Interval using the approximate Z

[X[bar] ± Z_{1-\alpha /2} * S/√n]

Z_{1-\alpha /2} = Z_{0.95} = 1.64

[37.7± 1.64* 9.2/√100]

[36.19;39.21]

b. You need to test if the population mean is greater than 35 with a level of significance of 1%.

The hypothesis is:

H₀: μ ≤ 35

H₁: μ > 35

α: 0.01

This is a one-tailed test so you have only one critical level (right tail):

Z_{1\alpha } = Z_{0.99} = 2.33

This means that if the value of the calculated statistic is equal or greater than 2.33 you will reject the null Hypothesis.

If the value is less than 2.33 you will support the null hypothesis.

The statistic is:

Z=<u> X[bar] - μ </u>= <u> 37.7 - 35 </u> = 2.93

       S/√n           9.2/10

The value 2.93 > 2.33, so you reject the null hypothesis. This means that the population mean of users that are connected at the same time is greater than 35.

<u><em>Note: </em></u><em>To make the decision using the interval calculated on a), the hypothesis should have been two-tailed and the confidence and significance levels complementary.</em>

I hope it helps!

You might be interested in
Please look for the question in the picture.
Ymorist [56]

it will be c

as

negative with negative erased together

5 0
2 years ago
Britany sends between 10 and 20 text messages per day. Each text message costs $0.80. Suppose Britany's cellular bill spans a pe
Dafna11 [192]
Well if its between 10 & 20 take the median which is 15 and multiple it by the about of days which is 56 and you get 840 dollars <span />
3 0
3 years ago
Find the equation of the line.<br> Use exact numbers.
allochka39001 [22]

Answer:

y = 2/3x+4

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
at a pet store 24% of the animal were dogs. If there are a total of 62 animals at the pet store, write a proportion that can be
Marysya12 [62]
Is/of = %/100
x/62 = 24/100
Where x is the number of dogs and 62 is the total number of animals. 24 is the percent of dogs which is out of 100 percent of all the animals.
4 0
2 years ago
What is the coefficient of the term 6x/7
AysviL [449]
A. 6x/7 = (6/7)x
These are equal
6 0
3 years ago
Other questions:
  • Tom can paint a house in 10 hours. If Sally helps, it takes them 4 hours. Without help, how long would it take Sally to paint a
    5·1 answer
  • you buy 6 apples for 2.70. write an equation that can be used to express the relationship between the total price t and the numb
    10·1 answer
  • Coffee: A popular chain of cafes has been receiving online complaints about one store location. Regular customers complained tha
    14·1 answer
  • Help asap! what does sinø=
    13·1 answer
  • Find the area of the figure​
    11·1 answer
  • Please someone help!5m^2 - 26m -24 =0
    12·1 answer
  • Greg paid $33 for 2 shirts and $48 for 3 shirts including a fixed shipping fee assuming the same function applies to any numbers
    11·1 answer
  • Help with math hw please
    8·1 answer
  • It won't let me copy the question but I linked a screenshot of it.
    6·1 answer
  • Please Help Me Please
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!