MA3110: Module 3 Sampling Distribution and Confidence
Interval
Exercise 3.2
Sample Mean Distribution and T-Interval
1
Task 1: Read the following case study, titled âGreen M&Mâsâ:
Green M&Mâs: Consider a class of 20 statistics students,
where each student is given 5 small bags of M&Mâs and asked to count the
number of green M&Mâs. The results are shown below. The population mean is
for a bag of this size is 10.06 and the population standard deviation is 2.59.
Bag 1 Bag 2 Bag 3 Bag 4 Bag 5
Bag
1
Bag 2
Bag 3 Bag 4
Bag 5
Student 1
3
4
7
6
14
Student 2
12
14
18
8
3
Student 3
12
18
8
13
11
Student 4
18
12
7
11
8
Student 5
17
18
9
14
2
Student 6
3
10
14
9
13
Student 7
3
12
11
9
15
Student 8
6
2
3
18
11
Student 9
8
16
12
17
3
Student 10
14
13
11
17
5
Student 11
3
14
17
17
15
Student 12
7
14
11
7
2
Student 13
17
2
12
18
13
Student 14
9
18
8
11
10
Student 15
14
16
4
3
12
Student 16
4
3
7
11
14
Student 17
11
17
6
5
13
Student 18
15
8
17
11
10
Student 19
4
9
13
16
16
Student 20
12
12
5
14
16
Answer the following questions:
a. Find the sample means for each studentâs green M&M
count.
MA3110: Module 3 Sampling Distribution and Confidence
Interval
Exercise 3.2
Sample Mean Distribution and T-Interval
2
b. Create a histogram of the sample means, and calculate the
mean and standard deviation of the
sample means. To construct a histogram, follow the given
steps:
I. Obtain a frequency (relative-frequency, percent)
distribution of the data.
II. Draw a horizontal axis on which to place the bars and a
vertical axis on which to display the
frequencies (relative frequencies, percents).
III. For each class, construct a vertical bar whose height
equals the frequency (relative
frequency, percent) of that class.
IV. Label the bars with the classes, the horizontal axis
with the name of the variable, and the
vertical axis with âFrequencyâ (âRelative frequency,â
âPercentâ).
Source: Weiss, Neil A. (2014: 2024 – Essay Writing Service. Custom Essay Services Cheap). Elementary Statistics (8th
ed.). Upper Saddle River, NJ: Pearson.
c. Theoretically, what are the mean, standard deviation, and
distribution of all possible sample means
for a sample size of 5?
Task 2: Read the following case study, titled âDiamond
Pricingâ:
In a Singapore Edition of Business Times, diamond pricing
was explored. The price of a diamond is based on
the diamondâs weight, color, and clarity. A simple random
sample of 18 one-half-carat diamonds had the
following prices, in dollars:
1676 1442 1995 1718 1826 2071 1947 1983 2146
1995 1876 2032 1988 2071 2234 2108 1941 2316
Based on the above information, solve the following
problems:
a. Apply the t-interval procedure to these data to find a
90% confidence interval for the mean price of
all one-half-carat diamonds. Interpret your result. (Note: x
? $1964.7 and s ? $206.5.)
Obtain a normal probability plot, a boxplot, a histogram,
and a stem-and-leaf diagram of the data.
b. Based on your graphs from part (b), is it reasonable to
apply the t-interval procedure as you did in
part a? Explain your answer.
MA3110: Module 3 Sampling Distribution and Confidence
Interval
Exercise 3.2
Sample Mean Distribution and T-Interval
3
Submission Requirements:
? Submit the assignment in a Microsoft Word or Excel
document.
? Show detailed steps and provide appropriate rationale with
your answers.
Evaluation Criteria:
? Correctly answered each question
? Included appropriate steps or rationale to determine the
answer to each question
