Research Question

Research Question

Objectives:

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.

Vocabulary

Question

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?”

Poll

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?

• Yes, report to the store.

• Yes, report to manufacturer.

• Yes, report to the news media.

• No, not a big difference.

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.

Writing Null and Alternative Hypotheses in Word.

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

Ho: The true mean weight ... 

Ha: The true mean weight ...

*Note

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.

Multiple Choice

What are the null and alternative hypotheses for this conjecture:

The average of attorneys life span is greater than 25.4 years.

• Ho: The true mean of attorneys life span is greater or equal to 25.4 years.

• Ha: The true mean of the attorneys life span is less than 25.4 years.

• Ho: The true mean of attorneys life span is greater or equal to 25.4 years.

  Ha: The true mean of the attorneys life span is less than 25.4 years.

• Ho:The true mean of the attorneys life span is less than 25.4 years.

  Ha:The true mean of attorneys life span is greater or equal to 25.4 years.

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)

Using symbols to write Hypotheses

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

Ho:

Ha:

Multiple Choice

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: μ > .21

  Ha: μ < .21

Multiple Choice

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

• H₀: μ > 64"

  Hₐ: μ ≠ 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"

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).

Practice Writing Hypotheses

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.

End of Lesson

Remember to do your homework.