Question

For each of the following ten educated guesses, or research ideas: A) state the populations; B) state the null hypothesis; C) state a directional research hypothesis; D) state a nondirectional research hypothesis 1. A sample of rats in a laboratory is given an experimental drug intended to make them learn a maze faster than other rats. 2. Do French children whose parents are engineers score higher than French children in general on math ability? 3. Do people who experienced the 1994 Northridge earthquake have more or less selfconfidence that the general population? 4. A researcher wants to discover whether children's diets affect adult intelligence. Twenty years later, he gives an IQ test to children who ate a low-fat, low-carbohydrate diet and compared them with children who ate a low-fat, high-carbohydrate diet. 5. Dr. Wilson wants to find out whether men or women are better drivers. She sets up an obstacle course and records the number of errors made by the drivers. 6. Harriet has a hypothesis that higher grades are achieved by students who sit at the front of the classroom. With the help of her colleagues, she gathers information about seating arrangements and classroom grades. 7. Jenny and Sarah are having an argument. Jenny thinks that single people are more likely to own pets, for companionship. Sarah thinks that pets are more likely to be adopted into a family because "pets and kids go together." 8. Researchers have consistently found that people who have a "Type A" personality are more likely to suffer heart attacks than people who have a "Type B" personality. 9. Is the level of income for residents of North Hollywood higher than the level of income of the residence in the San Fernando Valley? 10. Do drivers delay their departure from a Parking spot if they notice that some other driver is waiting to take that parking spot?

Answer 1

In hypothesis testing, the null hypothesis assumes no effect or difference, while the alternative hypothesis suggests an effect or difference, sometimes in a specific direction. A random variable is what we measure in the test, and based on the p-value and significance level, we decide whether to reject the null hypothesis or not.

Step-by-step explanation:

In hypothesis testing, we address a research question by stating two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis typically represents the status quo or a statement of no effect or no difference. The alternative hypothesis is what the researcher aims to support, indicating an observed effect or difference. When conducting a hypothesis test, the random variable is what we measure or count in order to decide between these two hypotheses.

• Populations: These are the groups we are studying, which may be people, animals, objects, or events that we assume to be representative of a larger group.
• Null Hypothesis (H0): A statement positing that there is no significant effect or difference between the populations.
  
• Directional Research Hypothesis (Ha): Suggests a specific direction of effect or difference.
• Nondirectional Research Hypothesis: Implies that there may be an effect or difference, but does not specify the direction of this difference.
• Random Variable: This is a variable that takes on different numerical values that are determined by chance.
  

The test statistic is calculated from the data and is used to determine whether to reject the null hypothesis. The p-value is the probability of observing the collected data, or something more extreme, assuming the null hypothesis is true. Based on the p-value and a predefined significance level (alpha), we decide whether to reject or fail to reject the null hypothesis.

To illustrate, consider an example of a null and alternative hypothesis involving school expenditures. If an average spending of $530 is observed for science students compared to $380 for humanities students, we would form a null hypothesis that says there is no difference in spending between the two groups, and an alternative hypothesis that says science students spend more. If a statistical test reveals a significant difference at alpha = 0.05, we would reject the null hypothesis in favor of the alternative. Conversely, a non-significant result would mean failing to reject the null hypothesis.