Question

Suppose that a lecturer gives a 10-point quiz to a class of five students. The results of the quiz are 3, 1, 5, 9, and 7. For simplicity, assume that the five students are the population. Assume that all samples of size 2 are taken with replacement and the mean of each sample is found.

Questions:

- Calculate the population mean and standard deviation
- Suppose that you obtain at least 20 random samples of size 2. From data obtained by you, find a frequency distribution of sample means and draw a graph (namely, histogram) of the sample means.
- Confirm whether your histogram appears to be approximately normal.
- Calculate the mean of sample means and standard deviation of sample means.

Answer #1

Suppose the population consists of FIVE individuals and the
elements are: S= {3, 6, 9, 12, and 15} Obtain samples of size 3
(use counting rule). Obtain the population mean and variance,
sample means and variances of the distribution. Would the mean and
variance change if the sample size were to increase? Prepare two
excel tables.
a) In an excel table show the various samples (Table-1).
b) Calculate the population mean and variance (Table-1).
c) Calculate the sample mean and...

The results obtained by 25 students on Quiz 1 and Quiz 2 in a
previous Statistics class are summarized in the following
table.
Quiz 1 Quiz 2 Sample mean 77% 78% Sample standard deviation 13%
12%
Assuming both populations are normally distributed, are the
marks for the two quizzes equally variable or not (at 10%
significance level)?

Suppose you roll two twenty-five-sided dice. Let X1, X2 the
outcomes of the rolls of these two fair dice which can be viewed as
a random sample of size 2 from a uniform distribution on
integers.
a) What is population from which these random samples are drawn?
Find the mean (µ) and variance of this population (σ 2 )? Show your
calculations and results.
b) List all possible samples and calculate the value of the
sample mean ¯(X) and variance...

You are interested in estimating the average height in a class
of 100 students. In this class the mean height is 65 inches and the
standard deviation is 4 inches. You take a sample of size 16 and
compute the average (mean) height of the sample which is 64 inches.
If we are sampling with replacement, how many different samples
(keeping track of order) of size 16 are possible? (Do not compute
this, just explain how to compute it.)
What...

3.) Last year, I gave a quiz to 200 students. Suppose the
five-number summary of the grades was 41, 59, 66, 80, 91. Assume
that no two people received the same score. Use this five-number
summary to answer the following questions:
(a) How many students scored above 80?
(b) In our survey, 50 students scored below what grade?
4. Suppose that the mean amount of money that credit card
companies charge for a late fee is $150 with a standard...

Suppose we repeatedly take samples of size 100 from the
population distribution, calculate a sample mean each time, and
plot those sample means in a histogram. The histogram we created
would be an example of a (variable, population, distribution,
sampling distribution???) . According to the central limit theorem,
the histogram would have a shape that is approximately (left
skewed, right skewed or normal???) , with mean (give a
number???) and standard deviation (give a number??). The
standard deviation of the statistic under...

1. An intelligence quotient, or IQ, is a measurement of
intelligence derived from a standardized test such as the Stanford
Binet IQ test. Scores on the test are normal distribution with a
mean score of 100 and a standard deviation of 15.
Draw 1000 samples of size n=9 from the distribution of
IQ. Calculate the sample mean of all 1000 samples.
Draw the histogram for all sample means in. What is the
shape of the sample means?
Calculate mean of...

The heights of 1000 students are approximately normally
distributed with a mean of 174.5 centimeters and a standard
deviation of 6.9 centimeters. Suppose 200 random samples of size 25
are drawn from this population and the means recorded to the
nearest tenth of a centimeter. Determine (a) the mean and standard
deviation of the sampling distribution of X¯; (b) the number of
sample means that fall between 171 and 177 cm.

Suppose a professor gives an exam to a class of 40
students and the scores are as follows. (Type the
data set in StatCrunch.)
35
44
46
47
47
48
49
51
53
54
55
55
57
57
57
58
59
59
59
59
60
60
60
60
60
62
62
62
64
68
69
70
72
73
73
75
75
77
82
88
a. Find each of the
following:
Mean:
Median:
Standard deviation:
Z-score for a student who...

The mean balance that college students owe on their credit card
is $1096 with a standard deviation of $350. If all possible random
samples of size 144 are taken from this population, determine the
following:
a) name of the Sampling Distribution
b) mean and standard error of the sampling distribution of the
mean (use the correct name and symbol for each)
c) percent of sample means for a sample of 144 college students
that is greater than $1200
d) probability...

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