M303 Hypothesis Testing I
Where we are
Preliminary research stages: problem → actionable management problem → research objectives → research questions → hypotheses.
Decide on exploratory, descriptive, or causal research.
Secondary and primary data; observational and qualitative methods; surveys; sampling schemes; and sample size.
Prepare data; use descriptive statistics, simple and cross-tabulations, hypothesis tests, correlation, and regression; then recommend.
Learning Objectives
The need for, idea behind, and stages of hypothesis testing.
Distinguish null and alternative hypotheses and construct them for a marketing question.
When to use each t, F, or chi-square test.
Run the relevant t, F, and chi-square tests with the M303 Web Tools.
Explain the results of the different t, F, and chi-square tests.
Previous-class review
Data editing identifies problems in the data.
TOmissions, ambiguities, interviewer errors, and inconsistencies are common data problems.
TWe generally assign numerical values to closed-ended response categories.
TClosed-ended questions are generally more difficult to code than open-ended questions.
FA nominal variable with M levels requires M + 1 dummy variables.
FFor our regression models, nominal variables must be represented with dummy variables.
TDescriptive statistics summarize variables of interest.
TSimple tabulations document frequencies and percentages for a categorical variable.
TCross-tabulation variables can remain continuous without grouping.
FSimple tabulation divides a sample into groups to compare one variable across another.
FA sample mean of 4.4 looks encouraging
A Microsoft marketing manager asks a random sample of 50 customers in a self-administered survey whether the campaign changed their perceptions of PCs.
Compared with before the campaign, do customers view PCs more negatively, the same, or more positively?
Does 4.4 prove that perceptions improved?
The 50 sampled customers reported slightly more positive perceptions.
Sampling error can produce 4.4 even if the campaign had no population-level effect.
Hypothesis testing follows the scientific method
Average PC perception remains 4 after the campaign.
Observe 50 customers who saw the campaign.
Calculate how likely a mean like 4.4 would be if the claim were true.
If the result is rare—for example, less than a 5% chance—reject the claim; otherwise, fail to reject it.
The hypothesis-testing workflow
Write the null and alternative hypotheses clearly.
Match the test to the variables and research design.
Use the M303 Web Tools with the course data file.
Ask whether the result is significant at the preselected threshold, typically p < .05.
Reject H₀ when significant; otherwise, fail to reject H₀.
The p-value measures compatibility with the null
If p ≥ .05, fail to reject H₀. The threshold must be chosen before seeing the result.
Null and alternative hypotheses play different roles
“The campaign did not change average PC perceptions.”
“The campaign improved average PC perceptions.”
Write the null: mean comparisons
Mean liking for Tropicana is higher than for Florida’s Natural orange juice.
H₀: The two mean liking scores are equal.
The average age of target consumers is below 29.
H₀: The population mean age is 29.
Women choose Macs over PCs more often than men do.
H₀: Choice shares do not differ by gender.
Write the null: relationships
Consumers are more likely to purchase energy-efficient refrigerators.
H₀: Energy efficiency is not related to refrigerator purchase.
Liking for Victoria’s Secret increases with the frequency of television advertising exposure.
H₀: Liking does not depend on advertising exposure frequency.
The hypothesis clarifies the variables, the comparison, and whether the alternative is directional.
Variable structure determines the test
How many variables are involved?
Continuous or categorical?
If applicable, identify the dependent and independent variables.
One sample, paired observations, independent groups, or a categorical association?
In the PC campaign, the variable is one continuous 1–7 perception-change rating. When price drives demand, price is the independent variable and demand is the dependent variable.
Match the question to the test
One continuous variable compared with a hypothesized value.
Two continuous measurements from the same respondents.
A continuous outcome across two independent groups.
A continuous outcome across three or more independent groups.
Association between two categorical variables.
Which test? Time spent by gender group
A manager uses browser cookies to record entry and exit times, then calculates minutes spent in the web store before ordering. In the source scenario, shipping names are used to code two gender groups.
Does average time on the site differ between the two groups?
Continuous outcome · two independent categorical groups.
Which test? Advertising medium and success
The company must choose between local radio and local television offers. Based on its previous campaigns, each outcome is coded as successful or unsuccessful.
Does the advertising medium affect whether the campaign succeeds?
Categorical outcome · categorical medium.
Which test? KitKat vs. Twix
Each participant rates both KitKat and Twix on the same 1–11 favorability scale.
Do the two average brand evaluations differ?
Two continuous ratings · same participants.
Which test? Perception change vs. no change
Each respondent gives one perception-change rating on a 1–7 scale; 4 means no change.
Is the average rating different from 4?
One continuous variable · one benchmark.
Which test? Three tablet prototypes
Three prototypes differ in screen size, resolution, cameras, and other design features. Three independent groups of 10 participants each try one prototype for a week and then rate liking on a 1–11 scale.
Are the three mean liking scores equal?
Continuous outcome · three independent groups.
Check your understanding
A p-value is computed under the assumption that the null hypothesis is true.
TA larger p-value provides stronger evidence for rejecting H₀.
FThe alternative hypothesis describes no effect, no relationship, or no difference.
FHypothesis testing seeks evidence that can falsify H₀ in favor of Hₐ.
TIf the claim is “Tropicana has higher mean liking,” H₀ states that the mean liking scores are equal.
TThe test choice depends on the number, type, and relationship of the variables.
TWhich test? A new price benchmark
A client will change price only if consumers’ average rating exceeds 5.0 on a 7-point fairness scale. The sample mean is 5.5.
Which test evaluates whether the population mean is greater than 5?
One continuous outcome · benchmark of 5.
Which test? Age and amusement-park interest
A phone study records yes/no interest for 300 randomly selected people: 59 of 120 under age 18, 38 of 110 ages 18–25, and 21 of 70 over age 25 say yes.
Does interest differ by age group?
Interest and age group are both categorical.
Which test? Brand Y vs. Brand X
Embedded in a survey, each participant rates Brand X, Brand Y, and Brand Z on the same 11-point scale from very unfavorable to very favorable, with indifference at the midpoint. Brand Y is the focal brand.
Is mean favorability for Brand Y higher than for Brand X?
Two ratings · same participants · directional alternative.
One-sample t-test
One-sample t-test
Ask whether a population mean differs from, exceeds, or falls below a hypothesized value.
Choose the alternative before looking at the data
Hₐ: μ ≠ 4
The campaign changed average perception in either direction.
Hₐ: μ > 4
The campaign improved average perception.
Hₐ: μ < 4
The campaign reduced average perception.
Choose Hₐ from the research question—before looking at the sample or its p-value.
One-sample example: the campaign mean
After seeing the campaign, 50 respondents rate perception change on a 1–7 scale. Data file: PerceptionsofPCAftertheAD.xlsx on Canvas.
Sample mean = 4.4 · benchmark = 4
Hₐ: μ ≠ 4
Test whether average perception changed in either direction.
Run the test with the M303 Web Tools
Instructions and required data files will be posted on Canvas.
Open the hypothesis-testing tool and load the campaign-perception data.
Select the continuous perception variable and enter the null value: 4.
Choose the alternative direction: ≠, >, or <.
Run the test and record the sample mean, test statistic, and p-value.
Read the one-sample output
| Output | Perceptions after the ad | Comparison value |
|---|---|---|
| Mean | 4.4 | 4 |
| Variance | 7.469387755 | 0 |
| Observations | 50 | 50 |
| Hypothesized mean difference | 0 | |
| Degrees of freedom | 49 | |
| t statistic | 1.034909779 | |
| P(T ≤ t), one-tail | 0.15289588 | |
| t critical, one-tail | 1.676550893 | |
| P(T ≤ t), two-tail | 0.30579176 | |
| t critical, two-tail | 2.009575237 | |
Read the p-value in the correct tail
Use the two-tailed p-value for Hₐ: μ ≠ μ₀.
Use the right-tail p-value for Hₐ: μ > μ₀.
Use the left-tail p-value for Hₐ: μ < μ₀.
If p < 0.05, reject H₀. Otherwise, fail to reject H₀. Then state the conclusion in the language of the marketing question.
In-class exercise: promotion return
A marketing promotion costs $20 per customer. From the customer database, 1,000 promotion recipients are selected randomly in PurchaseBehavior.xlsx on Canvas to test whether average purchase spending exceeds the $20 cost and therefore produces a positive return.
Write H₀ and Hₐ. Then ask: what changes if the promotion costs $30?
H₀: μ = 20
Hₐ: μ > 20
For a $30 cost, replace the benchmark with 30.
To sum up
A sample result can differ from the population because of sampling error.
The p-value measures how compatible the observed result is with the null hypothesis.
State H₀ and Hₐ, choose the test from the variable structure, and choose the tail before examining results.
A one-sample t-test compares a sample mean with a specified population benchmark.