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?

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Definitions:

Death Benefit

A sum of money paid by an insurance policy or retirement plan to the beneficiary upon the death of the insured person or plan holder.

Losses

The negative financial impact that occurs when expenses exceed revenues, or due to unforeseen events or damages.

Mutual Mistake

An error shared by all parties in a contract, leading to a misunderstanding regarding a fundamental fact or element of the agreement.

Fraud

Deliberate deception or misrepresentation intended to result in an unfair or unlawful gain.