A local business offers test-taking courses for students who are planning to take the Graduate Recor

Daanish Wilcox

Daanish Wilcox

Answered question

2022-03-04

A local business offers test-taking courses for students who are planning to take the Graduate Record Examination (GRE) as part of their graduate school applications. The business promises to produce student test scores that are above the national average. You collect a random sample of 75 local students who have taken the course and calculate that their average GRE score is 1630 with a standard deviation of 320. The average GRE score for all students in the nation is 1590. Conduct a significance test at a=.05 to answer the research question: Does the course significantly improve local student GRE scores?
What are the test requirements/assumptions for this significance test? Check all that apply.
-Random Sample
-Normal Sampling Distribution
-Interval-ratio variable of GRE scores
With an alpha of .05, what is your critical score?

Answer & Explanation

Vikki Chapman

Vikki Chapman

Beginner2022-03-05Added 8 answers

The t-test is used when the population standard deviation (σ) is not known. In one sample t-test, the only concern would be that data should be normally distributed. The condition that is the most important condition for the use of t-test is that the data should be selected randomly from the population.
The test requirements/assumptions for this significance test are:
-Random Sample
-Normal Sampling Distribution
-Interval-ratio variable of GRE scores
Degrees of freedom is,
df =n-1=75-1=74
As the test is required to find whether the course significantly improves local student GRE scores, it means that alternative hypotheses should contain greater than sign.
It will be a one-tailed/right-tailed test.
The critical t value for 74 degrees of freedom and for 0.05 level of significance with the one-tailed test is 1.665707 or 1.666.
Thus, with an alpha of .05, your critical score is 1.666.

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