Question

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 6100 graduate management programs worldwide. The mean score for all testtakers is 550 with a standard deviation of 120. 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 550. She has a random sample of 250 college seniors in the Philippines interested in pursuing graduate management education take the GMAT. Suppose we know that GMAT scores are Normally distributed with a standard deviation =120 .
State the null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines.

Answer 1

Answer:

$H_{0}: \mu = 500\text{ GMAT score}\\H_A: \mu < 500\text{ GMAT score}$

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 550

Sample size, n = 250

Alpha, α = 0.05

Population standard deviation, σ = 120

The mean GMAT score for all test takers is 550.

The researcher believes that the mean scores in the Philippines who are interested in pursuing graduate management education will be less than 550.

We design the null and the alternate hypothesis

in the following manner:

$H_{0}: \mu = 500\text{ GMAT score}\\H_A: \mu < 500\text{ GMAT score}$

The null hypothesis states that the sample is taken from the population and have a mean score of 550, while the alternate hypothesis states the researcher's claim that the sample of Philippines does not belong to the population and have mean score less than 550.