Exploring Hypothesis Testing in IB Math

What is the primary purpose of hypothesis testing in statistics?

• To collect data from experiments or studies

• To confirm the researcher's initial assumptions without testing

• To determine if observed data can be explained by chance alone

• To prove that one variable causes changes in another

What does a t-test compare?

• Variances of two populations

• Means of two populations

• Proportions of a single sample

• Independence of two categorical variables

Which test is appropriate for comparing the means of two different groups?

• ANOVA

• Two-sample t-test

• Chi-square goodness-of-fit test

• Chi-squared test of independence

Which test would you use to analyze the relationship between two categorical variables?

• One-sample t-test

• Chi-squared test of independence

• Two-sample t-test

• Chi-square goodness-of-fit test

What is the purpose of the chi-square goodness-of-fit test?

• To assess if sample data has normal distribution

• To determine if two variables are related

• To check if observed frequencies match expected frequencies

• To compare means of more than two groups

In hypothesis testing, what does the null hypothesis represent?

• The assumption that there is a significant effect or difference

• The prediction made by the researcher

• The status quo that there is no effect or difference

• The alternative hypothesis that is tested against the null

When conducting a hypothesis test, what is the first step in the process?

• Defining the null and alternative hypotheses

• Calculating the test statistic

• Determining the significance level

• Collecting the sample data

What is the significance level in hypothesis testing?

• The standard deviation of the sample data

• The level of mean difference expected in the test

• The threshold below which the null hypothesis is rejected

• The probability of incorrectly accepting the null hypothesis

What does a p-value indicate in hypothesis testing?

• The probability of the null hypothesis being true given the data

• The variance explained by the model

• The probability of the alternative hypothesis being false

• The likelihood of making a Type I error

How is the decision to reject the null hypothesis typically influenced?

• By the sample size

• By the researcher's bias

• By comparing the p-value to the significance level

• By the type of data collected