ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD

(Department of Business Administration)

WARNING

1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2. SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”.

Course: Statistical Inference (8417) Semester: Spring, 2025

Level: BBA (4 Years)

Total Marks:100 Pass Marks: 50

ASSIGNMENT No. 1

Q. 1 Discuss the importance of measures of central tendency in summarizing data and describe how to choose the most appropriate measure for different datasets.

For the datasets 5, 8, 12, 15, and 20, calculate the range, interquartile range, and coefficient of variation (20)

Q. 2 A survey sample of 150 people has a mean age of 35 years with a standard deviation of 5 years. Construct a 95% confidence interval for the mean age of the population.

Explain the importance of sampling in statistics and discuss the advantages of stratified sampling over random sampling. (20)

Q. 3 Differentiate between point estimation and interval estimation, and explain the role of confidence intervals in decision-making.

Estimate the required sample size needed to achieve a margin of error of 2% with a confidence level of 95%, given a population standard deviation of 10. (20)

Q. 4 Explain the role of null and alternative hypotheses in hypothesis testing and describe the possible errors in hypothesis testing.

A company claims that the average lifespan of their product is 5 years. A sample of 30 products has an average lifespan of 4.8 years with a standard deviation of 0.5 years. Test the hypothesis at a 5% significance level. (20)

Q. 5 Two factories produce light bulbs. A sample of 50 bulbs from Factory A has an average lifespan of 1,200 hours with a standard deviation of 100 hours. A sample of 50 bulbs from Factory B has an average lifespan of 1,180 hours with a standard deviation of 120 hours. Test whether there is a significant difference in the average lifespans of the bulbs at a 5% significance level.

Compare and contrast independent sample t-tests and paired sample
t-tests, and discuss when each should be used. (20)

ASSIGNMENT No. 2

Total Marks: 100 Pass Marks: 50

This assignment is a research-oriented activity. You are required to prepare a detailed report of about 3000 words on the topic allotted to you to be submitted to your teacher for evaluation.

You are required to select one of the following topics according to the last digit of your registration number. For example, if your registration number is 18-IDM-3427183 then you will select topic # 3(the last digit): -

List of Topics:

1. Descriptive Statistics
2. Probability
3. Probability Sampling Distribution
4. ANOVA
5. Non-Probability Sampling Distribution
6. Hypothesis Testing: One Sample Test
7. Hypothesis Testing: Two-Sample Test
8. Chi-Square
9. Non-parametric Methods
10. Time Series Forecasting

GUIDELINES FOR ASSIGNMENT # 2:

• 1.5 line spacing
• Use headers and subheads throughout all sections
• Organization of ideas
• Writing skills (spelling, grammar, punctuation)
• Professionalism (readability and general appearance)
• Do more than repeat the text
• Express a point of view and defend it.

STATISTICAL INFERENCE

(OUTLINES)

UNIT 1: DESCRIPTIVE STATISTICS

- Measures of Central Tendency

- Mean (arithmetic, weighted and geometric means)

- Median

- Mode

• Choosing Measures of Central Tendency
• Percentiles, Deciles, and Quartiles
• Measures of Dispersion

- Range and Semi-Interquartile Range

• Variance
• Standard Deviation
• The Coefficient of Variation
• Interpretations
• Skewness and Kurtosis
• Measures of Skewness and Peakedness

UNIT 2: SAMPLING AND SAMPLING DISTRIBUTION

• Population and Samples
• Parameters and Estimates
• Introduction to Statistical Inference
• Introduction to Sampling
• Importance of Sampling in Statistics
• Random Sampling
• Stratified and Proportional Stratified Sampling
• Other Sampling Procedures
• Errors in Sampling
• Sampling Distribution
• Point and Interval Estimation
• Using Sampling Distribution to make Inferences
• The relationship between sample size and Standard Error

UNIT 3: ESTIMATION

• Point Estimation
• Methods of obtaining Point Estimator
• Interval Estimation and Confidence Intervals
• Estimation of Means
• Estimation of Differences Between Means
• Estimation of Proportions
• Estimation of Variances
• Estimating the required Sample Size

UNIT 4: TESTING HYPOTHESES: ONE SAMPLE TESTS

• Role of Statistical Hypothesis
• Formulating Hypothesis
• The Null Hypothesis and Error Type
• Testing Hypothesis of means when population standard deviation is known.
• Measuring Power of Hypothesis Test
• Hypothesis Testing of Proportions- Large Samples
• Testing Hypothesis of means when population standard deviation is not known.

UNIT 5: TESTING HYPOTHESES: TWO SAMPLE TESTS

• Testing for differences between Means and Proportions
• Testing for differences between Means: Large Sample Size
• Testing for differences between Means: Small Sample Size
• Testing for differences between Means with Dependent Samples
• Testing for differences between Proportions: Large Sample Size
• Probability Value: Another way of looking at testing hypotheses

UNIT 6: Chi-Square and Analysis of Variance

• Chi-Square as a Test of Independence
• Chi-Square as Test of Goodness of Fit
• Analysis of Variance
• Inference about a Population Variance
• Inference about Two Population Variances

UNIT 7: REGRESSION AND CORRELATION ANALYSIS

• Estimation Using the Regression Line
• Correlation Analysis
• Inferences about Population Parameters
• Limitations, Errors, Caveats of Regression and Correlation
• Multiples Regression and Correlation Analysis
• Finding the Multiple Regression Equation
• Making Inferences about Population Parameters
• Modeling Techniques

UNIT 8: NONPARAMETRIC METHODS

• Introduction to nonparametric statistics
• The sign test for paired data
• Rank Sum Tests: The Mann-Whitney U Test and The Kruskal-Wallis Test
• One Sample Run Test
• Rank Correlation Test
• The Kolmogorov-Smirnov Test
• Factors affecting the Correlation

UNIT 9: TIME SERIES & FORECASTING

• Introduction to Time Series
• Variations in Time Series
• Trend Analysis
• Cyclical Variation
• Seasonal Variation
• Irregular Variation
• Time Series Analysis in Forecasting

Levin, R. I., & Rubin, D. S. (2009). Statistics for Management (7^th ed.). Delhi, India: Dorling Kindersley Ltd (under the license of Pearson Education).

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2005). Statistical Techniques in Business and Economics (12^th ed.). USA: McGraw-Hill Irwin

Holcomb, Jr. (2010). Mathematics with Applications in Management, Natural, and Social Sciences (10^th ed.). USA: Adison Wesley Publishers.

James, T. M., Benson, P. G., & Sincich, T. (2010). Statistics for Business and Economics (11^th ed.). USA: Prentice Hall.

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