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Cloud [144]
3 years ago
10

According to a recent​ survey, the population distribution of number of years of education for​ self-employed individuals in a c

ertain region has a mean of 13.5 and a standard deviation of 2.8. a. Identify the random variable X whose distribution is described here. b. Find the mean and the standard deviation of the sampling distribution of x overbar for a random sample of size 49. Interpret them. c. Repeat​ (b) for nequals196. Describe the effect of increasing n.
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0

Answer:

a) X: number of years of education

b) Sample mean = 13.5, Sample standard deviation = 0.4

c) Sample mean = 13.5, Sample standard deviation = 0.2

d) Decrease the sample standard deviation

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 13.5 years

Standard deviation,σ = 2.8 years

a) random variable X

X: number of years of education

Central limit theorem:

If large random samples are drawn from population with mean \mu and standard deviation \sigma, then the distribution of sample mean will be normally distributed with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

b) mean and the standard for a random sample of size 49

\mu_{\bar{x}} = \mu = 13.5\\\\\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}} = \dfrac{2.8}{\sqrt{49}} = 0.4

c) mean and the standard for a random sample of size 196

\mu_{\bar{x}} = \mu = 13.5\\\\\sigma_{\bar{x}} = \dfrac{\sigma}{\sqrt{n}} = \dfrac{2.8}{\sqrt{196}} = 0.2

d) Effect of increasing n

As the sample size increases, the standard error that is the sample standard deviation decreases. Thus, quadrupling sample size will half the standard deviation.

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