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A Shoe Company Designed a Low-Top and High-Top Version of a Particular

question 69

Essay

A shoe company designed a low-top and high-top version of a particular shoe. One of the shoe-making engineers claims that the low-top version does not last as long as the high-top version before wearing out. To test this claim, she takes a sample of 36 low-top and 64 high-top wearers and asks each the length of time before their shoes wore out. She finds that the low-tops wore out in an average of 140 days, and the high-tops wore out in an average of 150 days. Suppose the population standard deviation for both is 20 days.
A) Specify the competing hypotheses to determine whether high-tops last longer than low-tops for this particular shoe.
B) Calculate the value of the relevant test statistic.
C) Compute the p-value. Does the evidence support the commentator's claim at the 1% significance level?

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Definitions:

Price of Food

The monetary value assigned to food products, influenced by factors such as production costs, supply and demand.

Rotation

The act of turning around a center or an axis, often used metaphorically to describe a systematical shift in processes or roles.

Budget Line

A graphical depiction of all possible combinations of two goods that a consumer can purchase with a given income and prices.

Price of Food

The cost at which food items are sold, determined by various factors including supply, demand, production costs, and market conditions.