Preliminary Data Analyses Indicates That Use of a Paired T-Test $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

question 30

Essay

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-A coach uses a new technique in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below. $$\begin{array} { r | r r r r r r r r } \text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\ \hline \text { Before } & 109.7 & 112.3 & 109.5 & 118.3 & 111.1 & 120 & 117.1 & 114.6 \\ \hline \text { After } & 110.3 & 111 & 107.1 & 119.1 & 109.3 & 120.1 & 113.5 & 110.7 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters? Use the critical-value approach.

Understand the various methods used for predicting or analyzing market trends.

Recognize the importance of customer assessment and how it differs from other marketing methods.

Identify different research methods used in understanding customer behavior and needs.

Differentiate between qualitative and quantitative data in market research.

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Definitions:

Biological

Pertaining to the science of life or living organisms, including their structure, function, growth, evolution, and distribution.

Psychological

Pertaining to the scientific study of the mind and behavior, including cognitive, emotional, and social processes.

Vague Sense

A feeling or perception that is not clear, definite, or strongly formed.

Age of Six Months

A period marking six months of age, a developmental milestone in infants characterized by growth and the beginning of solid food introduction.