GRE Subject Test: Math : Probability & Statistics
Study concepts, example questions & explanations for GRE Subject Test: Math
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Example Questions
Example Question #3 : How To Find Z Scores For A Data Set
Natalie took her university placement examinations in Spanish and math. In Spanish, she scored 82; in math, she scored 86. The results of the Spanish exam had a mean of 72 and a standard deviation of 8. The results of the math exam had a mean of 68 and a standard deviation of 12. On which exam did Natalie do better, compared with the rest of her peers taking these placement exams?
The Math exam
She did equally well on both exams
The Spanish exam
None of the other answers, as z-scores cannot be calculated for this question
The Math exam
We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:
Her z-score for the Spanish exam is 
Example Question #1 : How To Find Z Scores For A Data Set
This year's harvest, the apples had a mean mass of 
What is the z-score of the apple you picked?
To find the z-score, we follow the formula
For this problem we see that
Substituting for these values we see
Example Question #112 : Other Topics
A bread maker has an average life of 9 years, with a variance of 4 years. What is the z-score associated with the probability that a bread maker lasts less than 13 years?
X is the test statistic we are looking to find. In this problem it is the probability that the bread maker lasts less than 13 years.
If you were to find the value associated with a z-score of 2 on the z-table, you would see that
Example Question #1 : Measures Of Distributions
The purpose of the t test is to do which of the following?
Describe the variance within a population.
Compare the significance of multiple variables.
Test the relationship between five or more variables.
Determine the ability of one variable to predict another.
Compare the means of separate populations.
Compare the means of separate populations.
A t test is used to compare the means of different groups. A t test score describes the likelihood that the difference in means between two groups is due to chance. The null hypothesis assumes the two sets are equal however, one can reject the null hypothesis with a p value within a particular confidence level.
Example Question #1 : Continuous Distributions
If 
Use the fact that the sum of 
Example Question #1 : Confidence Intervals
A sample of 
Find the 
Because we are only given the sample standard deviation we will use the t-distribution to calculate the confidence interval.
Appropriate Formula:
Now we must identify our variables:
We must find the appropriate t-value based on the given
t-value at 90% confidence:
Look up t-value for 0.05, 55 , so t-value= ~ 1.6735
90% CI becomes:
Example Question #1 : Confidence Intervals
|
Subject |
Horn Length (in) |
Subject |
Horn Length (in) |
|
1 |
19.1 |
11 |
11.6 |
|
2 |
14.7 |
12 |
18.5 |
|
3 |
10.2 |
13 |
28.7 |
|
4 |
16.1 |
14 |
15.3 |
|
5 |
13.9 |
15 |
13.5 |
|
6 |
12.0 |
16 |
7.7 |
|
7 |
20.7 |
17 |
17.2 |
|
8 |
8.6 |
18 |
19.0 |
|
9 |
24.2 |
19 |
20.9 |
|
10 |
17.3 |
20 |
21.3 |
The data above represents measurements of the horn lengths of African water buffalo that were raised on calcium supplements. Construct a 95% confidence interval for the population mean for horn length after supplments.
First you must calculate the sample mean and sample standard deviation of the sample.
Because we do not know the population standard deviation we will use the t-distribution to calculate the confidence intervals. We must use standard error in this formula because we are working with the standard deviation of the sampling distribution.
Formula:
To find the appropriate t-value for 95% confidence interval:
Look up 
Thus the 95% confidence interval is:
Example Question #1 : Confidence Intervals
The 
What does the confidence interval tell us about the difference in the two programs?
Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.
The confidence interval is large, so one program is clearly better at reducing mile times than the other.
The mean improvement of 
Zero is not in the interval, so reject the null. This is evidence that one program is significantly better at reducing mile times.
Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.
For there to be a statistically significant difference in the training programs, the 95% confidence interval cannot include zero. 
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All GRE Subject Test: Math Resources
