Research Question

Learning Objective:

Student will be able to write in words and in symbols the null and alternative hypotheses.

Language Objective:

Student will express their reasoning in written form.

And what about the Question box? 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:

“Do Spud Potato Chips contain an average of 28.3 grams of chips per bag?”

In some situations, researchers are even more formal and state hypotheses. In a case like this, the null hypothesis (Ho) generally states that there is no difference between the true value and the claimed value. The alternative hypothesis (Ha) 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 ... 

Ha: The true mean weight ...

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), population does not refer to people, but to bags of potato chips.

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)

x = the sample mean (pronounced x-bar)

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

Ho:

Ha:

Statistical studies are designed with carefully selected measures that ensure (within error margins) that, if the sample is well selected and the study is well designed and conducted, the mean and other measures of the sample are likely to be similar to the corresponding measures of the population being studied. Sometimes, if the population is small (such as high school seniors in a small town), it may be possible that the sample studied is the entire population. However, often a sample is a smaller subset of a population (such as a research question that might target the entire population of high school seniors in a state or in the nation).

Write them in words and then convert them to symbols.

A local pizza shop advertises “an average delivery time of 20 minutes or less,” but it does not offer a guarantee such as a free pizza. The national manager, Su Lin, wonders if her employees are fulfilling the claim.

Remember to do your homework.