Hypothesis Test
Definition
A hypothesis test is a statistical procedure used to make decisions about whether there is enough evidence to support or reject a claim about a population parameter. It involves formulating null and alternative hypotheses, collecting data, and using statistical tests to evaluate those hypotheses.
Analogy
Think of hypothesis testing like being on trial for a crime. The null hypothesis assumes innocence (no effect or no difference), while the alternative hypothesis suggests guilt (an effect or difference). Just like in court, we collect evidence (data) and use statistical tests as our "jury" to determine if there's enough evidence to convict (reject) or not convict (fail to reject) the null hypothesis.
Related terms
Type I Error: Type I error occurs when we reject the null hypothesis even though it is actually true. In other words, we mistakenly conclude there is an effect or difference when there isn't one.
Type II Error: Type II error occurs when we fail to reject the null hypothesis even though it is false. In other words, we miss detecting an effect or difference that actually exists.
P-value: The p-value is the probability of obtaining a test statistic as extreme as (or more extreme than) the observed value, assuming the null hypothesis is true. It helps us determine if our results are statistically significant.
"Hypothesis Test" appears in:
Study guides (3)
Additional resources (2)
Practice Questions (20+)
What should we include in a conclusion of a hypothesis test?
What is the primary basis for making a conclusion in a hypothesis test using the p-value?
A psychologist wants to investigate if there is a significant difference in anxiety levels before and after a treatment. He collects data from a random sample of 50 individuals and wants to conduct a hypothesis test. Which of the following procedures is most appropriate for him to use?
If the parameter in question is the mean, which type of hypothesis test should be used?
How can a z-score be used to conclude a hypothesis test?
In a hypothesis test, a z-score of -1.5 is obtained. What is the appropriate conclusion?
In a hypothesis test, the p-value is calculated to be 0.18. What is the appropriate conclusion at a significance level of α = 0.10?
In a hypothesis test, the calculated z-score is 2.1. What is the appropriate conclusion?
How can a small p-value affect the conclusion in a hypothesis test?
In a hypothesis test, a z-score of 3.2 is obtained. What is the appropriate conclusion?
In a hypothesis test, the calculated p-value is 0.07. What is the appropriate conclusion at a significance level of α = 0.05?
What does a large z-score indicate in a hypothesis test?
A researcher conducted a hypothesis test and obtained a p-value of 0.03. Based on this result, what decision should be made?
A pharmaceutical company wants to determine if a new drug is effective in reducing blood pressure. They conduct a study where they measure the blood pressure of a group of participants before and after administering the drug. Each participant serves as their own control. Which hypothesis test would be most appropriate for this scenario?
In a hypothesis test, if the p-value is less than the significance level, what should you do?
A researcher wants to compare the average weights of two different groups of individuals. The weights of the individuals in both groups are normally distributed. The researcher has collected independent samples from each group. Which hypothesis test would be most appropriate for this scenario?
What does it mean if the claim falls within the confidence interval in a hypothesis test?
When performing a hypothesis test, what determines whether it is a one-tailed or two-tailed test?
A statistics student is conducting a hypothesis test for the difference in two population proportions. They calculate a p-value of 0.02. What can they conclude?
A researcher is conducting a hypothesis test to determine if there is evidence to support the claim that the mean score of students who participated in a test prep program is higher than the mean score of students who did not participate. The p-value for the test is found to be extremely low. What may the researcher be able to conclude?
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