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?

• 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:

Angiotensin II

Peptide derived from angiotensin I; stimulates vasoconstriction and aldosterone secretion; also called active angiotensin.

Blood Volume

The total volume of blood circulating within an individual's vascular system.

ADH Production

The synthesis and release of antidiuretic hormone, also known as vasopressin, primarily by the posterior pituitary gland, which helps regulate water balance in the body.

Hyperventilation

Rapid or deep breathing that leads to a decrease in carbon dioxide levels in the blood, potentially causing dizziness or tingling.