Respuesta :
Given Information:
Population mean = p = 60% = 0.60
Population size = N = 7400
Sample size = n = 50
Required Information:
Sample mean = μ = ?
standard deviation = σ = ?
Answer:
Sample mean = μ = 0.60
standard deviation = σ = 0.069
Step-by-step explanation:
We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10
np ≥ 10
50*0.60 ≥ 10
30 ≥ 10 (satisfied)
n(1 - p) ≥ 10
50(1 - 0.60) ≥ 10
50(0.40) ≥ 10
20 ≥ 10 (satisfied)
The mean of the sampling distribution will be same as population mean that is
Sample mean = p = μ = 0.60
The standard deviation for this sampling distribution is given by
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
Where p is the population mean that is proportion of female students and n is the sample size.
[tex]\sigma = \sqrt{\frac{0.60(1-0.60)}{50} }\\\\\sigma = \sqrt{\frac{0.60(0.40)}{50} }\\\\\sigma = \sqrt{\frac{0.24}{50} }\\\\\sigma = \sqrt{0.0048} }\\\\\sigma = 0.069[/tex]
Therefore, the standard deviation of the sampling distribution is 0.069.
The mean and standard deviation of the given sampling distribution are respectively; μ = 0.60 and σ = 0.069
What is the mean and standard error?
We are given;
Population mean; p = 60% = 0.60
Population size; N = 7400
Sample size; n = 50
From the central limit theorem, the sampling distribution is approximately normal shown below to be equal or greater than 10,
np ≥ 10
50 × 0.60 ≥ 10
30 ≥ 10 (okay)
n(1 - p) ≥ 10
50(1 - 0.60) ≥ 10
50(0.40) ≥ 10
20 ≥ 10 (okay)
The mean of the sampling distribution will be same as population mean in this regards. Thus; Sample mean; p = μ = 0.60
The standard deviation for this sampling distribution is given by the formula;σ = √(p(1 - p)/n)
σ = √(0.6(1 - 0.6)/50)
σ = 0.069
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