A streaming platform wants to prove that its new subscription model has lowered the churn rate below the industry average of 6%.  A random sample of churn rates from 15 test markets is collected, and the following code produces a p-value of 0.001. Based on this test result, their churn is still the same as the industry average.

A retail analyst finds a positive correlation between holiday decorations in stores and monthly revenue. Why is it problematic to conclude that decorations are the sole cause of the revenue increase?

A fast food chain wants to assess performance by store location and menu item, using color to represent profit margins. Their goal is to quickly identify which combinations are underperforming. What chart would be most appropriate?

A company surveys 25 customers and wants to calculate a confidence interval for the average satisfaction score using bootstrapping. How many values should be in each resampled dataset?

An online clothing store has noticed that many shoppers abandon their cart at the final checkout screen. The team wants to understand what’s confusing or frustrating about the process. What VOC method would give the clearest insight into the issue?

A clothing manufacturer has a target of 12 minutes to stitch a pair of jeans. After implementing a new sewing process, they collect a sample of 25 jeans and calculate an average stitch time of 11.6 minutes. A one-sample t-test returns a p-value of 0.21. What is the most appropriate interpretation?

A wellness startup launches a meditation app aimed at busy professionals who feel overwhelmed and want more balance in their lives. What type of market segmentation is being used?

Multiply the matrices, and enter the values for a through d.   a:  b:  c:  d: 

A fitness device company launches a new version of its product with stress monitoring features based on customer feedback. What element of the marketing mix does this represent?

A company wants to compare damage rates between two packaging options: plastic bins and cardboard boxes. After shipping 50 items in each type, a two-sample t-test results in a p-value of 0.034. What is the most appropriate interpretation?