Question

1. Are the following statements TRUE or FALSE?:

(a) According to the Central Limit Theorem, given a large sample
size (*N* > 30), then a normal probability plot of the
same data would necessarily follow a straight line.

(b) A 95% confidence interval for a population mean that does not include zero would also mean that a hypothesis test on the same data would yield a significant result at the .05 level.

(c) The mean of a *t*-distribution with 5 degrees of
freedom is equal to the mean of a standard normal distribution.

(d) The sum of squared deviations from the mean is always equal to 0.

(e) The Empirical Rule is suitable for a *t*-distribution
with 500 degrees of freedom.

(f) The standard deviation of the sampling distribution of
x̄ is *σ*.

(g) A histogram is appropriate for summarizing data about political party affiliation.

(h) The degrees of freedom for a two-sample independent
*t*-test is *N* – 2

Answer #1

a) False, the normal probability plot of the same data will be follow symmetric bell-shaped curve.

b) it's depend on the hypothesis that if H0: popln mean = 0 , and alternative hypothesis is two sided then hypothesis test on the same data would yield a significant result at the 0.05 level.

c) True, for n=5, mean = 0 and also for standard normal distribution mean = 0.

d) false,

e) true sense for lajane t distribution approaches to normal distribution.

f) false the standard deviation of the sampling distribution of x.bar = sigma/✓n

g) False, histogram is used to plot the frequency of score occurrences in a continuous data set that has been divided into classes. bar chart is best option here.

h) False, it is n1+n2-2

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.

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...

True or False:
___________ According to the Central Limit Theorem, the sampling
distribution of means approximates a normal distribution given
sample sizes greater than 30.
___________ According to the textbook, single sample t-tests are
used instead of single sample z-tests when the population standard
deviation (σ) is unknown.
___________ A set of events is said to be mutually exclusive
when it contains all possible outcomes.
___________ Two-tailed tests predict the direction of the
effect

What is wrong with the following statement of the central limit
theorem?
Central Limit Theorem. If the random variables X1,
X2, X3, …, Xn are a random sample of size n from any distribution
with finite mean μ and variance σ2, then the distribution of will
be approximately normal, with a standard deviation of σ / √n.

10. For a particular scenario, we wish to test the hypothesis
H0 : p = 0.52. For a sample of size
50, the sample proportion p̂ is 0.42. Compute the value of
the test statistic zobs. (Express your answer
as a decimal rounded to two decimal places.)
4. For a hypothesis test of
H0 : μ = 8
vs.
H0 : μ > 8,
the sample mean of the data is computed to be 8.24. The
population standard deviation is...

Which of the following is NOT a conclusion of the Central Limit
Theorem? Choose the correct answer below.
A. The distribution of the sample means x overbar will, as the
sample size increases, approach a normal distribution.
B. The mean of all sample means is the population mean mu.
C. The distribution of the sample data will approach a normal
distribution as the sample size increases.
D. The standard deviation of all sample means is the population
standard deviation divided...

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.

The Central Limit Theorem is used when dealing with: mean from a
sample, individual data point ,chi-squared distributions, or
sampling distribution of a standard deviation? When using the CLT,
we use σ √ n for the: standard deviation for individual values,
mean for the sample, standard deviation of the sample means, or
sample size?

The following blood-type frequencies were obtained from a sample
of 1000 subjects.
Blood Type:
O
A
B
AB
Total
Frequency:
465
394
96
45
1000
An appropriate hypothesis test is conducted to test whether the
data is consistent with the claim that in this population, blood
types O, A, B and AB have proportions 0.45, 0.4, 0.1, and 0.05,
respectively. The resultant test statistic and associated p-value
are 1.25 and 0.741 respectively.
The test statistic should be compared to which...

Determine if the statements below are true or false:
The chi-square distribution, just like the normal distribution,
has two parameters, mean and standard deviation.
The chi-square distribution is always right skewed, regardless
of the value of the degrees of freedom parameter.
The chi-square statistic is always positive.
As the degrees of freedom increases, the shape of the chi-square
distribution becomes more skewed.
"If you found χ2 = 10 with df = 5, you would fail to reject the
Null hypothesis...

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