A Sample of 37 Students Enroll in a Program That $\bar { x } = 19$

question 22

Short Answer

A sample of 37 students enroll in a program that claims to improve scores on the quantitative reasoning portion of the Graduate Record Examination (GRE). The participants take a mock GRE test before the program begins and again at the end to measure their improvement The mean number of points improved wa $\bar { x } = 19$ . Assume the standard deviation is $\sigma = 58$ and let $\mu$ be the population mean number of points improved. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ .
i). Compute the value of the test statistic.
ii). Compute the $P$ -value.
iii). Do you reject $H _ { 0 }$ at the $\alpha = 0.05$ level?

Comprehend and calculate variance, including understanding its properties and relationship to standard deviation.

Understand the concepts and calculations related to coefficient of variation and correlation.

Interpret and analyze data summaries, including five number summaries and box plots.

Apply the concept of relative frequency in the context of data analysis.

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Definitions:

Drawn Out

Prolonged over time or made to last longer than necessary, often referring to events or processes.

Consumption Decisions

Choices made by individuals or households on purchasing goods and services with their available income.

Current Income

Income received by an individual or entity within a specified period of time, such as wages, salaries, or investment income.

Average Income

The amount of income earned per person in a given area or country, calculated by dividing the total income of a population by the number of people in that population.