ETF1100 Chap.6 Hypothesis Tests for Business Decisions
Hypothesis Tests for Business Decisions
Hypothesis Tests for Business Decisions turns a population claim into null and alternative hypotheses, selects a one-sided or two-sided direction, computes a standardised statistic and interprets the p-value under the null model. The chapter links rejection decisions to Type I and Type II errors and separates statistical significance from effect size and operational importance.
What this chapter covers
- 01
Null and alternative hypotheses
- 02
One-sided and two-sided tests
- 03
Test statistics and reference models
- 04
P-values and significance levels
- 05
Type I and Type II errors
- 06
Population conclusions and effect size
Worked example · free
Test whether a mean exceeds a target
- 1State H0: mu = 6 and H1: mu greater than 6.
- 1Compute SE = 2.1 / sqrt(49) = 0.30 minute.
- 1Compute z = (6.8 - 6.0) / 0.30 = 2.67.
- 1Use the right-tail p-value, approximately 0.0038.
- 1Reject the null because 0.0038 is below 0.05.
- 1Conclude that the population mean exceeds the target under the sampling conditions.
Key terms
- Null Hypothesis
- The benchmark population claim assumed when calibrating a test statistic and p-value.
- Alternative Hypothesis
- The population claim supported when the sample is sufficiently inconsistent with the null.
- Significance Level
- The chosen long-run Type I error threshold used for the rejection decision.
- P-value
- The probability under the null model of a result at least as extreme as observed.
- Type I Error
- Rejecting a true null hypothesis.
- Type II Error
- Failing to reject a false null hypothesis.
Hypothesis Tests for Business Decisions FAQ
What does a small p-value mean?
It means the observed result, or something more extreme, would be unusual under the null model. When the p-value is at most the chosen significance level, reject the null in favour of the stated alternative. It is not the probability that the null is true.
When should I use a one-sided test?
Use it when the business claim specifies a direction before the data are examined, such as a mean above a target or a defect rate below a benchmark. Use two sides when any difference matters. Do not choose the tail after seeing the sample.
Does failing to reject prove the null?
No. It means the sample provides insufficient evidence for the alternative under the chosen design and level. The effect may be small, the sample noisy or the study underpowered. Report the estimate and interval when available to show plausible effect sizes.
When should the significance level be chosen?
Choose alpha before inspecting the sample result so the rejection rule reflects the planned false-alarm tolerance rather than the observed p-value. If business error costs motivate a different threshold, document that reasoning separately. Moving alpha after seeing the data hides the intended error trade-off and weakens the calibration.
Exam move
Use a six-part test checklist drawn from the course rubric: hypotheses, assumptions, justified method, test statistic, p-value decision and population conclusion. Translate claim words such as exceeds, below and differs into the alternative before using Excel. Practise explaining a p-value with the phrase under the null model, then remove any wording that treats it as the probability of a hypothesis.
Build a two-by-two error table and attach a concrete business consequence to each error, because the relative costs inform the threshold. After every decision, report the observed effect size and ask whether it is operationally important. For automatic numeric entries, identify whether the box requests a standard error, statistic, p-value or endpoint. Keep full precision through the reference calculation.
Finish with the represented population and avoid causal language unless the study design supports it. A large p-value never licenses the phrase proven equal. For each practice claim, highlight the parameter, benchmark and direction before looking at the sample. Write the hypotheses in symbols and words, set alpha and predict which tail contains evidence. Only then calculate the standard error and statistic.
Sketch the reference distribution and place the observed statistic on it; this exposes a tail reversal before Excel returns a polished number. Interpret the p-value as a conditional probability of data at least as extreme under the null, never as the probability that a hypothesis is correct.
Build paired examples with the same p-value but different effect sizes and sample sizes so statistical evidence is not confused with operational importance. For error analysis, name the action associated with rejection, then describe the cost of acting on a true null and the cost of missing a false one.
Ask whether the sampling design supports independence and whether repeated customers, clustering or selection could make the nominal standard error too small. When a result is nonsignificant, inspect the confidence interval and identify effects that remain plausible instead of writing that nothing happened. When it is significant, report the estimated gap and a decision threshold rather than stopping at reject.
Complete the answer with method, conditions, statistic, probability statement, decision, population conclusion and practical consequence. This ordered workflow protects both the calculation and its meaning.
Working through Hypothesis Tests for Business Decisions in ETF1100? Sia is AskSia’s AI Statistics tutor — ask any ETF1100 Hypothesis Tests for Business Decisions question and get a clear, step-by-step explanation grounded in how ETF1100 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
