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puteri [66]
3 years ago
6

According to General Social Survey of 2016, the population distribution of number of years of education for self-employed indivi

duals in the United States has a mean of 12.9 and a standard deviation of 4.0. The distribution is skewed slightly to the right. For each sample size below: Describe the mean, standard error, and shape of the sampling distribution of the means for a random sample of: (7 pts) a) 16 residents b) 49 residents c) 121 residents Describe the pattern as n increases
Mathematics
1 answer:
nikdorinn [45]3 years ago
3 0

Answer:

a) Mean is 12.9

b) Standard Error

i) n = 16, Standard Error = 1

The shape of the sampling distribution means is not normal

ii) n = 49 , Standard Error = 0.5714285714

The shape of the sampling distribution means is normal

iii) n = 121, Standard Error = 0.3636363636

The shape of the sampling distribution means is normal

c)Describe the pattern as n increases

As the number of random samples(n) increases the value for the standard error decreases

Step-by-step explanation:

Central Limit Theorem states that

if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal.

a) 16 residents

Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√16

= 4/4

= 1

n < 30, hence, The shape of the sampling distribution means is not normal

b) 49 residents

= Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√49

= 4/7

= 0.5714285714

n > 30, hence, The shape of the sampling distribution means is normal

c) 121 residents

Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√121

= 4/11

= 0.3636363636

n > 30, hence, The shape of the sampling distribution means is normal

Describe the pattern as n increases

As the number of random samples(n) increases the value for the standard error decreases

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3 years ago
Match each power of a power expression with its simplified expression.
VARVARA [1.3K]

Answer:

> (4^6)^{-3} = \frac{1}{4 ^ {18}}

> (4^{-3})^{-3} = 4 ^ 9

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Step-by-step explanation:

We have to expand the powers of each of them:

> (4^6)^{-3} = 4^{(6 * -3)}

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(4^6)^{-3} = \frac{1}{4 ^ {18}}

> (4^{-3})^{-3} = 4 ^ {(-3 * -3)}

  (4^{-3})^{-3} = 4 ^ 9

> (4^0)^{-9} = 4 ^ {(0 * -9)}

  (4^0)^{-9} = 4 ^0

> (-4^{-9})^2 = -4 ^ {( -9 * 2)}

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8 0
2 years ago
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So, to find the mean you want o add up all of the numbers and then divide by the number of numbers.

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For the median you want o line all of your number up from least to greatest and then find the middle number.

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4 0
3 years ago
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