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2 years ago

True or False: When the length of a confidence interval is 3 for inference concerning a mean, the required sample size is4

1 answer:

6 0

If the length of a confidence interval is 3 for inference concerning a mean, the required sample size is $(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2$

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

σ = standard deviation, n = sample size, the margin of error (E) is given by:

$E=z_\frac{\alpha }{2}*\frac{\sigma}{\sqrt{n} } \\\\E=3, hence:\\\\3=z_\frac{\alpha }{2}*\frac{\sigma}{\sqrt{n} } \\\\n=(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2$

If the length of a confidence interval is 3 for inference concerning a mean, the required sample size is $(z_\frac{\alpha }{2}*\frac{\sigma}{3} )^2$

Find out more on equation at: brainly.com/question/2972832

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The letters of the alphabet are written on cars and placed in a brown paper bag. What is the probability of drawing a vowel, rep

Oksanka [162]

Answer:

25 / 676

Step-by-step explanation:

There are 5 vowels in the alphabets, and there are 26 alphabets in total as a whole.

The probability of drawing a vowel kb first trial is going to be

5 / 26, total number of vowels and total number of alphabets as a whole.

Again, we're told to replace the picked vowel, and pick another vowel, so that will once again be

5 / 26.

To get the final answer, we multiply both answers by each other

5 / 26 * 5 / 26 = 25 / 676.

Therefore, the probability has been found to be 25 / 676

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3 years ago

What is the scientific notation of 0.00165?

Ierofanga [76]

Answer:

The answer is $1.65*10^{-3}$

Step-by-step explanation:

when writing scientific notation, there must be one number to the left of the decimal point.

To achieve this in this problem, you need to move the decimal point 3 times to the right.

because you are moving the point to the right, the exponent will be negative.

*rule of thumb: moving the decimal to the left will give you a positive exponent, moving to the right will give you a negative exponent*

therefore you answer should be written as:

$1.65*10^{-3}$

hope this helps :)

6 0

2 years ago

What is 4.7 in a fraction into a simplest form

zhannawk [14.2K]

4.7 as a fraction would be 4 and 7/10 (7 over 10).

8 0

3 years ago

Read 2 more answers

Consider the expressions 7y + 5 − 3 and 7y + 2. Which statement is true?

romanna [79]

The two expressions are equivalent because they have the same value regardless of the number of substituted in for y

4 0

1 year ago

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

juin [17]

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= X[bar] - μ = 37.7 - 35 = 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.

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

I hope it helps!

7 0

2 years ago