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 6000 graduate management programs worldwide. the mean score for all test takers is 570, with a standard deviation of 125.
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 more than 570.
she has a random sample of 250 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 σ=125.
the null and alternative hypotheses are h0:μ=570 versus ha:μ>570.
another sample of 250 students had a sample mean (xbar) of 590. the p - value for this outcome is using the conservative method and using the tables in the text is
for this question, you will submit the work for this question within question 29. if you are using my excel spreadsheet, crunchit, or a ti calculator for any part of your work, you must include the output from these technologies in jpeg/jpg format, properly labeled, within your submission. only these technologies are allowed—no other excel spreadsheets should be used. upload the labeled output as part of your submission in a pdf or word document that contains your answers to all 28 questions. failure to include the required technology output may result in the loss of points. also include a screenshot of the table where you can locate your answer

Explanation:

Step1: Identify the test type

This is a one - sample z - test for the population mean. The formula for the z - statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Given: $\mu = 570$, $\bar{x}=590$, $\sigma = 125$, $n = 250$

Step2: Calculate the z - statistic

First, calculate the standard error $SE=\frac{\sigma}{\sqrt{n}}=\frac{125}{\sqrt{250}}\approx\frac{125}{15.8114}\approx7.91$

Then, calculate the z - statistic: $z=\frac{590 - 570}{7.91}=\frac{20}{7.91}\approx2.53$

Step3: Find the p - value

Since the alternative hypothesis is $H_{a}:\mu>570$, we need to find the area to the right of $z = 2.53$ under the standard normal curve.

Using the standard normal table or a calculator, the area to the left of $z = 2.53$ is approximately 0.9943. So the area to the right (the p - value) is $1 - 0.9943=0.0057$

Answer:

The p - value is approximately 0.0057.