The common assumptions made when doing a ttest include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size and equality of variance in standard deviation.
The TTest
The ttest was developed by a chemist working for the Guinness brewing company as a simple way to measure the consistent quality of stout. It was further developed and adapted, and now refers to any test of a statistical hypothesis in which the statistic being tested for is expected to correspond to a tdistribution if the null hypothesis is supported.
A ttest is an analysis of two populations means through the use of statistical examination; a ttest with two samples is commonly used with small sample sizes, testing the difference between the samples when the variances of two normal distributions are not known.
Tdistribution is basically any continuous probability distribution that arises from an estimation of the mean of a normally distributed population using a small sample size and an unknown standard deviation for the population. The null hypothesis is the default assumption that no relationship exists between two different measured phenomena. (For related reading, see: What does a strong null hypothesis mean?)
TTest Assumptions
The first assumption made regarding ttests concerns the scale of measurement. The assumption for a ttest is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test.
The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.
The third assumption is the data, when plotted, results in a normal distribution, bellshaped distribution curve.
The fourth assumption is a reasonably large sample size is used. A larger sample size means the distribution of results should approach a normal bellshaped curve.
The final assumption is homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.

What's the difference between a representative sample and a random sample?
Explore the differences between representative samples and random samples, and discover how they are often used in tandem ... Read Answer >> 
When is it better to use systematic over simple random sampling?
Learn when systematic sampling is better than simple random sampling, such as in the absence of data patterns and when there ... Read Answer >> 
What percentage of the population do you need in a representative sample?
Learn about representative samples and how they are used in conjunction with other strategies to create useful data with ... Read Answer >> 
What is the difference between a simple random sample and a stratified random sample?
Learn about the differences between simple random sampling and stratified random sampling, and the advantages of each method. Read Answer >> 
What are the disadvantages of using a simple random sample to approximate a larger ...
Learn what a simple random sample is, how researchers use it as a statistical tool and the disadvantages it carries when ... Read Answer >> 
What are the advantages and disadvantages of using systematic sampling?
Learn about the primary advantages and disadvantages of using a systematic sampling method when conducting research of a ... Read Answer >>

Investing
Hypothesis testing in finance: Concept and examples
When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics. 
Investing
How to Use Stratified Random Sampling
Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ... 
Investing
Style Matters In Financial Modeling
If you're looking to get a job as an analyst, you'll need to know how to work it. 
Investing
Returns and Financial Planning Projections
Return expectations continue to be a necessary part of any investment strategy discussion. 
Investing
Bet Smarter With the Monte Carlo Simulation
This technique can reduce uncertainty in estimating future outcomes. 
Investing
Lognormal and normal distribution
When and why do you use lognormal distribution or normal distribution for analyzing securities? Lognormal for stocks, normal for portfolio returns. 
Investing
How to use Monte Carlo simulation with GBM
Learn how to estimate risk with the use of a Monte Carlo simulation to predict future events through a series of random trials. 
Investing
Calculating The Equity Risk Premium
See the model in action with real data and evaluate whether its assumptions are valid. Here is how to calculate the equity risk premium. 
Trading
The linear regression of time and price
This investment strategy can help investors be successful by identifying price trends while eliminating human bias. 
Investing
How Vanguard Index Funds Work
Learn how Vanguard index funds work. See how the index sampling technique allows Vanguard to charge low expense ratios that can save investors money.

TTest
A statistical examination of two population means. A twosample ... 
ZTest
A ztest is a statistical test used to determine whether two ... 
Sampling Distribution
A sampling distribution is a probability distribution of a statistic ... 
Sample
A sample is a smaller, manageable version of a larger group. ... 
Alpha Risk
Alpha risk is the risk in a statistical test of rejecting a null ... 
Simple Random Sample
A subset of a statistical population in which each member of ...