The Graduate Management Admission Test (GMAT) is taken by individuals interested in pursuing graduate management education. GMAT scores are used as part of the admissions process for more than 60006000 graduate management programs worldwide. The mean sore for all test takers is 563,563, with a standard deviation of 118.of 118.
A researcher in the Philippines is concerned about the performance of undergraduates in the Philippines on the GMAT. She believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 563.563. She has a random sample of 250250 college seniors in the Philippines interested in pursuing graduate management education that take the GMAT. Suppose we know that GMAT scores are Normally distributed with standard deviation ?=118.deviation �=118.
The null and alternative hypotheses are ?0:?=563�0:�=563 versus ??:?<563.versus ��:�<563.
Data on scores on the GMAT can be found at www.gmac. com/gmat/learn-about-the-gmat-exam, www.gmac.com/gmat-other-assessments/ accessing-gmat-exam-scores-and-reports/ gmat-scoring-by-exam-section-normal-view, and www.gmac.com/market-intelligence-and-research/assessment-data/ about-the-geographic-trend-reports. The mean and standard deviation for the GMAT scores is based on data from 2015–2018 and is based on the results of 739, 752 tests.
One sample of 250 students had mean GMAT score ?⎯⎯⎯=555.�. Enter this ?⎯⎯⎯,�¯, along with the other required information, into the P-Value of a Test of Significance applet.
What is the ?-value?�-value? Give your answer to four decimal places.
?-value:�-value:
Is this outcome statistically significant at the ?=0.05 level? At the ?=0.01 level?
Another sample of 250 students had ?⎯⎯⎯=540.�. Use the applet to find the ?-value�-value for this outcome. Give your answer to four decimal places.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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