Hypothesis Testing: Mean and Types

Hypothesis Testing: Mean

• Hypothesis testing is a process for making objective decisions about a hypothesized parameter.
• Null hypothesis: an initial claim based on prior knowledge.
• Alternative hypothesis: what the researcher believes to be true.

Hypothesis Testing: Types

• Hypothesis testing mechanism is used to make an objective decision about a hypothesized parameter.
• Significance level (α): the margin of error assumed by the researcher.
• P-values: the data-based probability that the decision to reject the null hypothesis is wrong. It's compared to the significance level.

What Test and When?

• Tests based on number of variables: single vs two variables (or groups).
• Test type based on variables: tests comparing means (e.g., continuous variables), and tests for associations (e.g., continuous and categorical variables).
• Tests based on type of variables: comparing means (e.g., single mean, related samples T-test, unrelated samples T-test).

Comparing Means

• Helpful for determining if one group's (average) satisfaction differs from another.
• Useful to find out whether a change in a situation (e.g., introducing a new program) makes a difference.
• Example: Marvel movie consumers vs. DC movie consumers.
• Example: Effectiveness of a streaming service.
• Types of tests include T-tests (related, unrelated samples) and Chi-square.

Means Related Tests in Market Research

• Single mean: Test used to make a judgment about a population's mean, using a sample. Can be one or two tailed tests. Example: the average age of Kroger shoppers.
• Two unrelated samples: Used to compare two independent samples (groups). Example: comparing online vs. in-store shoppers.
• Two related samples: Used to compare one sample to itself (the same group) before and after a marketing action (e.g., before and after a marketing campaign). Example: measuring the effect of a free trial.

Unrelated vs Related Sample t-tests

• Unrelated sample: Analyzing loyalty between tech-savvy and non-tech-savvy customers, or differences between groups.
• Related sample: Observing changes in customer loyalty before and after a marketing campaign. Compares the same groups at different times.

Steps in Hypothesis Testing

• State the hypothesis: Defining the null and alternative hypothesis to help interpret results
• Select the statistical test: Choosing a hypothesis test based on correlations or comparisons.
• Determining decision based on t-test or P-value.
• Make a decision and conclusion.

One-tailed vs. Two-tailed

• One-tailed: Used when only interested whether a parameter is either larger or smaller than a predefined value.
• Two-tailed: Used to determine whether a parameter falls within certain upper or lower bounds.

Hypothesis Tests for Means

• Known population variance: Z-test used to test for differences in means if the population variance is known.
• Unknown population variance: T-test used to test for differences in means if the population variance isn't known.

Decision Rules for T-tests

• Determining whether to use a one or two-tailed test depends on the type of hypothesis being tested.

Explore the fundamentals of hypothesis testing, including null and alternative hypotheses. Learn about significance levels, P-values, and the appropriate tests based on the type and number of variables. This quiz will enhance your understanding of statistical decision-making.