It Starts with a Question

Consider this situation: "This unopened bag of chips is half empty. I wonder if it really contains 28.3 grams as the package says?"

This type of informal question or observation is the beginning of many investigations. Informal questions can turn into more formal problem statements or research questions.

For example, you may decide to investigate whether there is a scandal in the potato chip industry by checking the following:

Suppose you conduct the investigation into Spud Potato Chips and find that the mean weight of the chips in your sample is 25 grams, rather than 28.3 grams ( x = 25 grams). Do you think that a difference of 3.3 grams between the actual and advertised weights is large enough that it needs to be reported? If so, how do you report this information and to whom?

In some situations, researchers are even more formal and state hypotheses. In a case like this, the null hypothesis (H_o) generally states that there is no difference between the true value and the claimed value.
The alternative hypothesis (H_a) states that something is different or incorrect, or that something has changed.

What are the null and alternative hypotheses for the potato chip example?

Ho - The true mean weight of bags of Spud Potato Chips 28.3 grams or greater.

Ha - The true mean weight of bags of Spud potato chips is less than 28.3 grams.

text annotation indicator chips

Notice that the hypotheses say "The true mean weight." This implies that the statements refer to the population of all Spud Potato Chip bags, not just a single bag or even a small sample. When a statistical investigation is conducted, it generally employs a sample that is then used to make a generalization about the population. Notice that in this case (as in many cases), the population does not refer to people, but to bags of potato chips.

When researchers select and weigh a sample, they know the sample mean, but they plan to generalize to the population mean. When a numerical representation of a population is computed, it is generally called a population parameter. When a numerical representation of a sample is computed, it is called a sample statistic.

To be concise, researchers often use symbols in place of words. Greek letters are usually used when referring to populations (the entire group being studied, from which a sample or samples will be drawn). English letters are used for samples (the particular items or individuals included in a particular study). For example, when discussing the mean:

μ = the population mean (Greek letter mu—pronounced mew)
= the sample mean (pronounced x -bar)

So the hypotheses for a study can be stated in words or symbols. When using symbols, you must identify what your symbols represent.

Ho: μ ≥ 28.3 grams, where μ is the true mean weight of a bag of Spud Potato Chips

Ha: μ < 28.3 grams

It Starts with a Question Self Assessment

Problem 1¹, Problem 2¹, Problem 3², Problem 4², Problem 5³, Problem 6³Citations:

¹OpenStaxCollege. (2013, July 19). Null and Alternative Hypotheses – Introductory Statistics. Pressbooks. Retrieved October 14, 2022, from https://pressbooks-dev.oer.hawaii.edu/introductorystatistics/chapter/null-and-alternative-hypotheses/

²1.2 - Samples & Populations | STAT 200. (n.d.). PennState: Statistics Online Courses. Retrieved October 14, 2022, from https://online.stat.psu.edu/stat200/lesson/1/1.2

³Al., E. O. I. B. &. (n.d.). Appendix B: Practice Tests (1-4) and Final Exams | Introduction to Statistics. Retrieved October 14, 2022, from https://courses.lumenlearning.com/introstats1/chapter/appendix-b-practice-tests-1-4-and-final-exams/

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