Question

A sample mean 80 and sample standard deviation 12 for the random sample of 100
observations. The standard error of the mean is​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

The standard error of the mean measured is 0.12.

Step-by-step explanation:

Data given,

The mean of the sample, x = 80

The sample standard deviation, σ = 12

The total number of random sample observations, N = 100

To find:

The standard error of the mean, e =?

Now,

The percentage error of the mean can be calculated by the equation of the number of observations given below:

• $N = [\frac{C_{v} }{e}]^{2}$   ----------- equation (1)

Here,

• N = The total number of sample observations
• $C_{v}$ = The coefficient of variation
• e = The percentage error of the mean

Firstly, we have to calculate the coefficient of variation by the equation given below:

• $C_{v} = \frac{\sigma}{x} \times 100$

Here,

• σ = The standard deviation of the sample
• x = Mean of the sample

Therefore,

• $C_{v} = \frac{12}{80}\times 100$
• $C_{v}$ = 15%

Now, after putting the value of the coefficient of variation in equation (1), we get:

• $100 = [\frac{15 }{e}]^{2}$
• $e^{2} = \frac{225}{100}$
• $e^{2}$= 2.25e = 1.5

As we know,

• The standard error of the mean = mean × absolute mean error percentage

• The standard error of the mean = 80 ×$\frac{1.5}{100}$ = 0.12.