Question

(05.02 LC)

The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? (4 points)

I. The distribution of the sample mean is exactly Normal.

II. The distribution of the sample mean is approximately
Normal.

III. The standard deviation is equal to that of the
population.

IV. The distribution of the population is exactly Normal.

a |
I and II |

b |
I only |

c |
II and III |

d |
I, III, and IV |

e |
II only |

(05.01 MC)

Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂? (4 points)

a |
0.03 |

b |
0.02 |

c |
0.97 |

d |
0.94 |

e |
0.25 |

Answer #1

The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true?
The distribution of the sample mean is approximately
Normal.
The standard deviation is equal to that of the population.
The distribution of the population is exactly Normal.
The distribution is biased.

31) – (33): A random sample of size n = 40 is selected from a
population that has a proportion of successes p = 0.8.
31) Determine the mean proportion of the sampling distribution
of the sample proportion.
32) Determine the standard deviation of the sampling
distribution of the sample proportion, to 3 decimal places.
33) True or False? The sampling distribution of the sample
proportion is approximately normal.

A random sample of size n = 50 is selected from a
binomial distribution with population proportion
p = 0.8.
Describe the approximate shape of the sampling distribution of
p̂.
Calculate the mean and standard deviation (or standard error) of
the sampling distribution of p̂. (Round your standard
deviation to four decimal places.)
mean =
standard deviation =
Find the probability that the sample proportion p̂ is
less than 0.9. (Round your answer to four decimal places.)

A random sample of size n = 40 is selected from a binomial
distribution with population proportion p = 0.25. (a) What will be
the approximate shape of the sampling distribution of p̂?
approximately normal skewed symmetric Correct: Your answer is
correct. (b) What will be the mean and standard deviation (or
standard error) of the sampling distribution of p̂? (Round your
answers to four decimal places.) mean 0.25 Correct: Your answer is
correct. standard deviation 0.0685 Correct: Your answer...

A random sample of size n=80 is taken from a population of size
N = 600 with a population proportion p = 0.46.
What is the probability that the sample mean is less than
0.40?
Please provide an answer with 3 decimal
points.

Which one of the following statements is
true?
A. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for large n only if the distribution of the population is
normal.
B. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for small n only if the distribution of the population is
normal.
C. The Central Limit Theorem states that the sampling
distribution...

a) What is the Central Limit Theorem? It is always true
that as the sample size, n, increases, the distribution of the
sample means will be approximately normally distributed.
Explain
b) If the underlying population of study is not normally
distributed, how large should the sample size be? What if the
population is normally distributed ?

Which of the following statements is not consistent with
the Central Limit Theorem?
1. The Central Limit Theorem applies to non-normal population
distributions.
2. The standard deviation of the sampling distribution will be
equal to the population standard deviation.
3. The sampling distribution will be approximately normal when
the sample size is sufficiently large.
4. The mean of the sampling distribution will be equal to the
population mean.

Use the normal approximation to find the indicated probability.
The sample size is n, the population proportion of successes is p,
and X is the number of successes in the sample. n = 81, p = 0.5:
P(X ≥ 46)

A sample of size 81 is taken from a population with unknown mean
and standard deviation 4.5.
In a test of H0: μ = 5 vs. Ha: μ < 5,
if the sample mean was 4, which of the following is true?
(i) We would reject the null hypothesis at α = 0.01.
(ii) We would reject the null hypothesis at α = 0.05.
(iii) We would reject the null hypothesis at α = 0.10.
only (i)
only (iii)
both...

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