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 test‑takers 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 standard deviation σ = 120 .

State the null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines.

Answer 1

Null hypothesis:
`\mu_(Phil) \geq 550`

Alternative hypothesis:
`\mu_(Phil) < 550`

Explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

Let X the random variable that represent the score for all test‑takers and the distribution for X is:

`X \sim N(\mu =550,\sigma=120)`

Let
`\mu_(Phil)` the true mean for the Philippines.

On this case we want to test is
`\mu_(Phil)<550`

So the correct system of hypothesis for this case would be:

Null hypothesis:
`\mu_(Phil) \geq 550`

Alternative hypothesis:
`\mu_(Phil)< 550`

In order to test we know the population deviation and the sample size n=250. But we need the sample mean and a significance level to test the claim.