**Question A**

A marketing manager of a well-known bookstore in the UK conducted a survey measuring customers’ loyalty.

Customers’ Loyalty was measured with one question on an ordinal scale from 1 to 10, with lower values indicating less strength and higher values greater strength. The manager also took details on their gender.

The manager performed a t-test to examine whether there was an association between the variables loyalty and gender. The results are shown below.

Table. T-test results for loyalty between male and females. Grouping variable was gender. The mean difference expresses: (male’s mean – female’s mean).

**1.** How many types of t-tests do we have? Please, write what you know for each type.

**2.** What are the assumptions of t-tests? Give examples.

**3.** What is the difference between a null hypothesis H0, and an alternative hypothesis,H1? What is the null hypothesis and the alternative hypothesis in this question?

**4.** Is loyalty significantly associated with gender? Why? Please, specify your answer.

**5.** The mean difference between the two groups is -0.86. What does this mean?

**Question B**

Service bundling is the practice of marketing two or more services in a single package. For example, Virgin Media’s bundle package includes Broadband, Digital TV, Calls package and Line rental. Marketers spend billions of dollars each year to promote service bundles by emphasizing incentives such as savings discounts, convenient billing options, and free gifts.A group of researchers from the US1 studied the effects of bundle incentives on 300 consumers’ perceived value, search intentions for alternative service providers, and switching intentions to a competitor.

Perceived Value, Switching Intentions and Search intentions were measured on a continuous scale.

Service Bundles was a categorical variable with three categories:

• Unbundled

• Bundled – convenience only

• Bundled – 10% Savings discount

The authors used one-way ANOVAs to examine the effect of bundles types on Perceived Value, Switching Intentions and Search Intentions.

**1.** What is ANOVA? How many types do you know? Please, specify your answer.

**2.** Did bundle type affect significantly any of the continuous variables? Comment on the p- value.

**3.** Which continuous variable do you think bundle type affects more? Comment on the F value.

**4.** The posthoc mean differences for perceived value between bundle types are shown in the below table:

Please comment on the significance and the signs of each paired differences.

**5.** In your opinion, do bundled services increase customer’s perceived value for the product?

**Question C**

An experiment has a single factor with four groups and eight values in each group.

**1.** If SSA = 70 and SST = 190, what is SSW?

**2.** What is MSA?

**3.** What is MSW?

**4.** What is the value of FSTAT?

**5.** At the 0.05 significance level (Fa = 3.89) what is your statistical decision? Please, give a detailed explanation.

**Question D**

A | B | TOTAL | |

YES | 40 | 25 | 65 |

NO | 35 | 45 | 80 |

TOTAL | 75 | 70 | 145 |

**1.** Compute the expected frequency for each cell.

**2.**Compute χ² STAT. Is it significant at α = 0.01 (χ²0.01 = 9.2103)? Please, give a detailed explanation.

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