Question

The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153. What is the value of the test statistic used to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average

Answer 1

The value of the test statistic used to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average = 2.33

Explanation:

To compute the test statistic for this question, we would be calculating the z-statistic because we have information about the population standard deviation

So, we compute the z-test statistic

z = (x - μ)/σₓ

x = sample mean = 153

μ = standard to be compared against = 150

σₓ = standard error of the mean = (σ/√n]

σ = population standard deviation = 9

n = Sample size = 49

σₓ = (9/√49) = 1.2857

z = (153 - 150) ÷ 1.2857

z = 2.333333 = 2.33

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