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- MATH 1342

### MATH 1342

# Elementary Statistical Methods

### Math 1342

**State Approval Code:**27.0501.51 19**Semester Credit Hours:**3**Lecture Hours per Week:**3**Contact Hours per Semester:**48

### Catalog Description

Collection, analysis, presentation and interpretation of data, and probability. Analysis includes descriptive statistics, correlation and regression, confidence inervals and hypothesis testing. Use of appropriate technology is recommended. (2705015119) (3-3-0) (fall, spring, summer 1 or 2)

### Prerequisites

### Course Curriculum

### Basic Intellectual Compentencies in the Core Curriculum

- Reading
- Listening
- Critical thinking

### Perspectives in the Core Curriculum

- Use logical reasoning in problem solving.

### Core Components and Related Exemplary Educational Objectives

### Mathematics

- To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
- To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
- To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
- To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize the limitations of mathematical and statistical models.
- To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

### Instructional Goals and Purposes

Panola College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.

### General Course Objectives

Upon successful completion of this course, the student will:

- Explain the use of data collection and statistics as tools to reach reasonable conclusions.
- Recognize, examine and interpret the basic principles of describing and presenting data.
- Compute and interpret empirical and theorectical probabilites using the rules of probabilities and combinatorics.
- Explain the role of probability in statistics.
- Examine, analyze and compare various sampling distributions for both descrete and continuous random variables.
- Describe and compute confidence intervals.
- Solve linear regression and correlation problems.
- Perform hypothesis tesing using statistical methods.

### Specific Course Objectives

Upon completion of **MATH 1342**, the student will be able to demonstrate:

- Define and/or explain the concepts of vocabulary, terminology, and notation used in this course.
- Create a frequency table from a set of data, and draw a histogram from this table. Perform analysis of histograms.
- Create a pie graph, a pareto chart, a scatter-plot, and a stem and leaf plot from a set of data, either by hand or using statistical software. Perform analysis of different charts constructed.
- Compute mean, median, mode, midrange, variance, and standard deviation of data sets. Compare and contrast the measures of center.
- Compute the z-score and percentile of a given score of data sets.
- Compute the probability of a simple and compound events. Use critical thinking to interpret the results.
- Summarize the results of a probability procedure in a probability distribution. Calculate the mean, variance, and standard deviation of a probability distribution.
- Find the probabilities associated with binomial distributions. Find the mean, variance, and standard deviation of a binomial distribution.
- Find the probabilities associated normal distributions.
- Construct a confidence interval for mean, proportion, and standard deviation or variance and use critical thinking to interpret the results. Determine the sample size necessary to estimate the mean, proportion, and variance.
- Test a hypothesis about a mean, proportion, and standard deviation or variance and use critical thinking to interpret the results.
- Find the linear correlation coefficient, perform a hypothesis test for linear correlation, and find the equation of the regression line of a linearly correlated set of data. Use critical thinking to interpret the results.

### General Description of Each Lecture or Discussion

After studying the material presented in the text(s), lecture, laboratory, computer
tutorials, and other resources, the student should be able to complete all behavioral/learning
objectives listed below with a minimum competency of 70%.** **

**1. Define and/or explain the concepts of vocabulary, terminology, and notation used
in this course.**

1.1 Define: statistic, parameter, population, sample, census, quantitative, qualitative, continuous numerical data, discrete numerical data, mean, median, mode, midrange, range, standard variance, z-score, percentile, event, simple event, sample space, independent events, dependent events, addition rule, multiplication rule.

1.2 Explain the concept of: nominal, ordinal, interval, ratio, random sampling, convenience sampling, cluster sampling, systematic sampling, stratified sampling, the range of probability values, classical and relative frequency approach to probability, subjective probability, law of large numbers, requirements for a probability distribution, unusual probability, disjoint events, independent and dependent events, complementary events, 2 requirements of a probability distribution, 4 requirements for a binomial probability distribution, the normal probability distribution, the Student’s t distribution, the chi-square distribution, confidence intervals, and hypothesis testing.

1.3 Be able to identify: Σ, μ, σ, σ^{2}, N, s, s^{2}, P(A), n, x, p, q, p, P(x), α, H_{0}, H_{1}, ρ, r

**2.**** Create a frequency distribution from a set of data, and draw a histogram from this
table. Perform analysis of histograms.**

2.1. Given a set of data, create a frequency distribution.

2.2. Modify a frequency distribution to create a relative frequency distribution and a cumulative frequency distribution.

2.3. Given a frequency distribution, identify the class limits, class width, class midpoints, class boundaries, and the sample size.

2.4. Given a frequency distribution create a frequency histogram.

2.5 Given a relative frequency distribution create a relative frequency histogram.

2.6. Analyze a histogram.

**3. Create a pie graph, a pareto chart, a scatter-plot, and a stem and leaf plot
from a set of data, either by hand or using statistical software. Perform analysis
of different charts.**

3.1. Construct a stem and leaf plot from a set of numerical data and given a stem and leaf plot, reconstruct the original set of data.

3.2. Construct a pie chart from a set of non-numerical data using computer software.

3.4. Construct a scatter-plot using Statdisk computer software.

3.5. Analyze stem and leaf as to the distribution of data.

3.6. Compare a pie graph and a pareto chart for ease of construction and presentation.

3.7. Analyze trend of a scatter-plot.

**4. Compute mean, median, mode, midrange, variance, and standard deviation of data
sets. Compare and contrast the measures of center.**

4.1. Calculate the mean, median, mode, and midrange using the definitions and formula.

4.2. Calculate the mean, median, and midrange using lists on the TI-83/84 calculator.

4.3. Analyze the effect of an extreme value in a data set on the mean, median, and midrange.

4.4 Calculate the range, standard deviation, and variance as a class exercise using the definitions and formulas.

4.5. Calculate the range, standard deviation, and variance using lists on the TI-83/84 calculator.

4.6. Analyze the effect of an extreme value in a data set on the standard deviation.

4.7. Apply the empirical rule given the mean and standard deviation of a data set.

4.8. Calculate the mean and standard deviation of a frequency distribution using lists
on the TI-83/84 calculator.** **

**5. Compute the z-score and percentile of a given score of data sets**.

5.1. Calculate the z-score of a data point.

5.2. Compare standardized scores (z-scores) and analyze what a z-score means.

5.3 Calculate the percentile of a data point and explain the results.

5.4. Find P_{k} in a ordered data set.

**6. Compute the probability of a simple and compound events. Use critical thinking
to interpret the results.**

6.1 Set up and calculate a simple probability.

6.2. Given information about a population or sample, be able to put it in a 2-way table.

6.3. Find the probability of simple events by using the information from the 2-way table.

6.4. Find the probability of events joined by the word ** or** or

**by using information from the 2-way table.**

*and*6.5. Find the probability of a sequence of independent events using key words** all** and

*both.*6.6. Find the probability of a sequence of dependent events using key words** all** and

*both.*6.7. Determine whether probabilities are unusual by comparing them to 0.05.

**7.**** Summarize the results of a probability procedure in a probability distribution. Calculate
the mean, variance, and standard deviation of a probability distribution.**

7.1. Determine if a distribution is a probability distribution by seeing if it meets the two requirements of probability distributions.

7.2. Summarize the results of a probability procedure in a probability distribution; make sure the resulting distribution meets the two requirements.

7.3. Find the mean, standard deviation, and variance of a probability distribution using the formulas or lists on the TI 83/84 calculator.

7.4. Find the expected value (mean) of a probability distribution using the formula or lists on the TI 83/84 calculator.

**8.**** Find the probabilities associated with binomial distributions. Find the mean, variance,
and standard deviation of a binomial distribution.**

8.1. List the 4 requirements for binomial procedures.

8.2. Calculate binomial probability as an in-class activity using the binomial formula.

8.3. Calculate binomial probability using binompdf, binomcdf, and 1-binomcdf on the TI 83/84 calculator.

8.4. Calculate the mean, variance, and standard deviation of a binomial distribution.

**9.**** Find the probabilities associated normal distributions.**

9.1. Relate the concept of area to the sum of the probabilities of a sample space.

9.2. Draw the normal curve marking the mean and three standard deviations to the left and right of the mean.

9.3. Relate the empirical rule (68, 95, 99.7%) to the normal distribution.

9.4. Describe the standard normal distribution giving its mean and standard deviation.

9.5. Define a z score.

9.6. Calculate probability for standard normal distributions and non-standard normal distributions using normalcdf on the TI-83/84 calculator.

9.7. Given a percent or percentile, find the corresponding value using invNorm on the TI-83/84 calculator.

9.8. Apply the Central Limit Theorem to appropriate problems.

9.9. Determine if a value is unusual relating to either probability or the range rule of thumb.

**10. Construct a confidence interval for mean, proportion, and standard deviation
or variance and use critical thinking to interpret the results. Determine the sample
size necessary to estimate the mean, proportion, and variance.**

10.1. Identify the best point estimate for μ, p, and σ^{2}.

10.2. Relate that α is the area in the tail(s) of a probability distribution and α is the probability that the parameter is not contained within the confidence interval.

10.3. Given the confidence interval find error and eithe rp-hat or x-bar.

10.4. Look up critical values on the z table or using invNorm and use to calculate error.

10.5. Calculate error and construct a confidence interval for a proportion and interpret what the confidence interval means.

10.6. Calculate error and construct a confidence interval for a mean when σ is known. Interpret what the confidence interval means.

10.7. Look up critical values on the students’ t probability distribution (or using invT) to calculate error and construct a confidence interval for a mean when σ is unknown. Interpret what the confidence interval means.

10.8. Look up critical values on the chi square probability distribution to construct a confidence interval for a standard deviation or variance. Interpret what the confidence interval means.

10.9. Use z score and formulas to calculate how large a sample must be taken to estimate a proportion or a mean.

10.10. Use table 7-2 to determine how large a sample must be taken to estimate a standard deviation or variance.

**11. Test a hypothesis about a mean, proportion, and standard deviation or variance
and use critical thinking to interpret the results.**

11.1. Given H_{0} or H_{1}, determine if the test is left tailed, right tailed or two tailed

11.2. Use the z, t, or χ^{2} distributions (or invNorm and invT) to identify critical values.

11.3. Calculate the z, t, or χ^{2} test statistics given formulas from the text.

11.4. Perform a test of hypothesis about a population proportion, a population mean, and a population standard deviation or variance using the traditional 8-step approach.

11.5. Summarize the results of the hypothesis test in the last step using critical thinking and a sample statement.

**12. Find the linear correlation coefficient, perform a hypothesis test for linear
correlation, and find the equation of the regression line of a linearly correlated
set of data. Use critical thinking to interpret the results.**

12.1. Plot paired data on a scatter-plot and visually try to determine linear correlation.

12.1. Look up r critical values on the Pearson’s correlation coefficient table.

12.2. Calculate the linear correlation coefficient r test statistic using lists on the TI-83/84 calculator.

12.3 Perform the 6-step traditional hypothesis test for linear correlation and summarize the results of the test in the last step using critical thinking and a sample statement.

12.4 Write the equation of the regression line using the capabilities of the TI-83/84 calculator.

12.5 If data is linearly correlated, use the regression line to predict a y value.

12.6 If data is not linearly correlated, use the mean of the ys to predict a y value.

### Methods of Instruction/Course Format/Delivery

Methods employed will include Lecture/demonstration, discussion, problem solving,
analysis, and reading assignments. The instructor will also use Canvas LMS for discussion,
demonstrations, and video presentation. *Homework will be assigned.*

### Assessment

- Attendance
- Class preparedness and participation
- Collaborative learning projects
- Exams/tests/quizzes
- Homework
- Canvas LMS and internet
- Scientific observations
- Student-teacher conferences
- Oral questioning in class
- Student presentations at the board

**Letter Grades for the Course will be assigned as follows:**

**A:** 90 < **Average** < 100

**B:** 80 < **Average** < 90

**C:** 70 < **Average** < 80

**D:** 60 < **Average** < 70

**F:** 00 < **Average** < 60

### Text, Required Readings, Materials, and Supplies

For current texts and materials, use the following link to access bookstore listings: Panola College Store