4.2 Hypothesis Testing

• What is the purpose of hypothesis testing?

  To support a claim
• What does the term 'significance level' (α) represent in hypothesis testing?

  Threshold to reject H₀
• The null hypothesis (H₀) represents the default assumption in hypothesis testing.


  True
• Choosing the appropriate test statistic is crucial for hypothesis testing
• Arrange the key steps in hypothesis testing:

  1️⃣ Formulate the hypotheses

  2️⃣ Choose the test statistic

  3️⃣ Set the significance level

  4️⃣ Calculate the p-value

  5️⃣ Make a decision
• What is the symbol for the alternative hypothesis?

  H₁
• In hypothesis testing, the null hypothesis represents the default assumption or the status quo
• Why is choosing the appropriate test statistic crucial for hypothesis testing?

  Depends on data and hypotheses
• The z-statistic is used for testing means when the data is continuous and the sample size is large
• After choosing the test statistic, the next step in hypothesis testing is to determine the critical values or p-value
• If the p-value is less than α, we reject the null hypothesis.


  True
• To make a decision in hypothesis testing, compare the p-value to the significance level α
• The p-value is the probability of observing the test statistic if H₀ is true.


  True
• Steps in hypothesis testing

  1️⃣ Formulate the hypotheses

  2️⃣ Choose the test statistic

  3️⃣ Set the significance level

  4️⃣ Calculate the p-value

  5️⃣ Make a decision
• What determines the choice of the appropriate test statistic?

  Data type and hypotheses
• What is the symbol for the null hypothesis in statistical testing?

  H₀
• Match the test statistic with its data type and hypotheses:

  t-statistic ↔️ Continuous, Testing means

  z-statistic ↔️ Continuous, Large sample size

  Chi-square statistic ↔️ Categorical, Independence or goodness of fit

  F-statistic ↔️ Continuous, Comparing variances
• Formulating hypotheses is the first step in hypothesis testing.

  True
• Match the hypothesis type with its definition:

  Null hypothesis ↔️ Default assumption or status quo

  Alternative hypothesis ↔️ Statement to be proven
• The alternative hypothesis is always a statement that we are trying to disprove.

  False
• Match the test statistic with its formula:

  t-statistic ↔️ t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}</latex>

  z-statistic ↔️ $z =$$\frac{\bar{x} - \mu_{0}}{\sigma / \sqrt{n}}$

  Chi-square statistic ↔️ $χ² =$$\sum \frac{(O_{i} - E_{i})^{2}}{E_{i}}$

  F-statistic ↔️ $F =$$\frac{s_{1}^{2}}{s_{2}^{2}}$
• What is the formula for the t-statistic?

  $t =$$\frac{\bar{x} - \mu_{0}}{s / \sqrt{n}}$
• The F-statistic is used for comparing variances of continuous data.


  True
• What is the significance level (α) in hypothesis testing?

  Predetermined probability threshold
• In hypothesis testing, α represents the probability of rejecting H₀
• The t-statistic is an example of a test
• Match the hypothesis type with its description:

  Null Hypothesis (H₀) ↔️ Default assumption presumed true

  Alternative Hypothesis (H₁) ↔️ Statement the test seeks to support
• The formula for the t-statistic is t = (\bar{x} - μ₀) / (s / √n)
• The t-statistic is used for testing hypotheses about means with continuous data.


  True
• Hypothesis testing involves setting up a null hypothesis (H₀) and an alternative hypothesis (H₁), which challenges the null
• The null hypothesis (H₀) represents the default assumption that is presumed true unless evidence suggests otherwise
• The z-statistic is used for large sample sizes when testing hypotheses about means.


  True
• Match the test statistic with its appropriate use:

  t-statistic ↔️ Testing means with continuous data

  z-statistic ↔️ Testing means with large samples

  Chi-square statistic ↔️ Testing independence or goodness of fit

  F-statistic ↔️ Comparing variances of continuous data
• What type of data is the chi-square statistic used for?

  Categorical
• What are critical values in hypothesis testing?

  Thresholds for rejecting H₀
• Steps to perform a hypothesis test:

  1️⃣ Calculate the test statistic

  2️⃣ Determine the critical region

  3️⃣ Compare the test statistic to critical values

  4️⃣ Make a decision

  5️⃣ Interpret the results
• If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

  True