Question

It has been reported that the mean score for a student who takes the certain test is 80 with the standard deviation of 0.9 . For a random sample of 100 students, what is the standard error
a 0.9
b 0.6
c 0.5
d 0.8​

Answer 1

Given : mean score for a student who takes the certain test is 80 with the standard deviation of 0.9

To Find : For a random sample of 100 students, what is the standard error

Solution:

Standard Error  =  standard deviation / √number of samples

n = number of samples

standard deviation = σ

SE = Standard Error

SE = σ / √n

σ = 0.9

n = 100

=> SE =  0.9 / √100

=> SE = 0.9/10

=> SE = 0.09

standard error is 0.09

None of the given option matches

If standard deviation  is given as 9

The SE = 9/10  = 0.9

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Answer 2

Answer:

The Standard Error with a random sample of 100, under the given circumstances, is 0.09.

Step-by-step explanation:

Given - the mean of the data = 80
             the standard deviation = 0.9

To find - the standard error, with a sample of 100 students

Formula - $Standard\;Error = \frac{\sigma}{\sqrt{n} }$

Solution -

We are given that $\sigma = 0.9\\n = 100$

Thus, we can calculate the Standard Error as follows -

$SE = \frac{\sigma}{\sqrt{n} } \\\\SE = \frac{0.9}{\sqrt{100} } \\\\SE = \frac{0.9}{10}$

Thus, we can write the SE to be 0.09.

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