22576 Chap.8 Hypothesis Development and t-Tests
Hypothesis Development and t-Tests
This chapter turns business questions into testable hypotheses.
It defines the null and alternative hypotheses, the two-tailed, left-tailed and right-tailed forms of the alternative, and the p-value decision against thresholds of 0.01, 0.05 and 0.1. It then matches tests to data: a one-sample t-test against a benchmark, an independent t-test for two separate groups, a paired t-test for repeated measures on the same people, and ANOVA for three or more groups.
The group brief requires t-tests among its descriptive techniques, and the sample presentation questions ask why a t-test suited the chosen variables.
This chapter therefore pairs the decision rule with the reasoning behind each test, so that you can defend the choice as well as run it, and write each conclusion with its direction, size and p-value.
What this chapter covers
- 01
Null and alternative hypotheses
- 02
Two-tailed, left-tailed and right-tailed alternatives
- 03
P-values and significance thresholds
- 04
Univariate, bivariate and multi-variable questions
- 05
One-sample, independent and paired t-tests
- 06
ANOVA for three or more groups
Worked example · free
Choose the test and the tail for three questions
- 1(a) One sample against a target value: one-sample t-test; 'below' makes it left-tailed.
- 1(b) Two separate groups of customers: independent t-test; 'differ' makes it two-tailed.
- 1(c) The same staff measured twice: paired t-test; 'higher after' makes it right-tailed for after minus before.
Key terms
- Null hypothesis
- The tentative position that there is no relationship, difference or effect.
- Paired t-test
- A test comparing two related measurements taken on the same individuals.
- ANOVA
- A method for comparing the means of three or more groups.
- Levene's test
- A check on whether two groups have equal variances, read before choosing the t-test row.
- Alternative hypothesis
- The claim that a significant difference or effect exists, the opposite of the null hypothesis.
- One-sample t-test
- A test of whether a sample mean differs from a stated benchmark value.
Hypothesis Development and t-Tests FAQ
How do I decide whether to reject the null hypothesis?
Compare the p-value with the threshold chosen in advance, usually 0.05, or 0.01 and 0.1 as alternatives. If the p-value is below the threshold, reject the null and support the alternative; otherwise report that the evidence is insufficient, rather than claiming the null has been proved.
What is the difference between a paired and an independent t-test?
A paired test compares two measurements on the same individuals, such as the credit limit each customer requested and the limit approved. An independent test compares two separate groups, such as single and married customers. Using the wrong one misstates the variability and can change the conclusion.
Why does Levene's test appear in the t-test output?
It checks whether the two groups have equal variances. If its p-value is above 0.05 there is no evidence the variances differ, so read the equal-variance result; if it is below, read the unequal-variance result. The tutorial reads Levene first for exactly this reason.
When should ANOVA be used instead of a t-test?
Use ANOVA when comparing the means of three or more groups, such as average satisfaction across several regions. A t-test compares two means at a time, so running many pairwise t-tests instead of one ANOVA complicates the comparison and the conclusion.
What makes a hypothesis testable?
It names the variables, the groups or benchmark, and the expected direction or difference clearly enough that data can support or reject it. 'Single customers spend less per year than married customers' is testable with an independent t-test; 'customers like our brand' is not, until it is tied to a measurable variable.
What does a p-value of 0.25 tell me?
That a difference as large as the one observed would be quite common by chance alone if the null hypothesis were true, so the evidence against the null is weak. At any of the usual thresholds of 0.01, 0.05 or 0.1, the null is not rejected and the result is reported as insufficient evidence.
Assessment move
Build a one-page decision card: data structure on one side, test and tail on the other, and drill it with invented business questions. Then rerun the three Week 6 t-tests in KNIME and write each conclusion with direction, size and p-value. For the group report, list each hypothesis beside the finding that suggested it, so the rubric's link from evidence to question is visible.
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