Question

In: Statistics and Probability

Describe the following sampling distributions. What are the means and standard errors, and are we guaranteed...

Describe the following sampling distributions. What are the means and standard errors, and are we guaranteed of normality?

a. μ = 20; σ = 4; n = 64

b. P = 70%; n = 30

Expert Solution

a)

Solution :

Given that,

mean = = 20

standard deviation = = 4

n = 64

The sampling distribution of mean is ,

= 20

The sampling distribution of standard deviation is ,

= / n = 4/ 65

= 0.4961

b)

Solution

Given that,

p = 70 % = 0.70

1 - p = 1 - 0.70 = 0.3

n = 30

The mean of the sampling distribution of proportion is ,

= p = 0.70

The standard error of the sampling distribution is ,

= $\sqrt$ [p( 1 - p ) / n = $\sqrt$ [0.70 (0.3) / 30] = 0.0837

= 0.0837

orchestra answered 2 years ago

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