t-Tests
In looking at your business, when and why would you want to use a one-sample mean test (either z or t) or a twosample t-test? Create a null and alternate hypothesis for one of these issues. How would you use the results?
A t-test is when the test statistic follows a t-distribution, and want to statistically test whether the
null hypothesis is true. T-Tests are used to test if the difference of means is statistically
significant. It tests if the sample is representative of the populations. For example, if the mean
for variable 1 is 20 and the mean for variable 2 is 28, we may say the means are different. TTests may show that they are not significantly different, however, and we can’t base our
conclusion on the means’ difference since the difference in the sample is not representative for
the population. Paired t-Test, also called dependent t test, are used when the data of variable 1
and data of variable 2 were collected in parallel from each individual, such as “before versus
after” cases. Suppose the marketer collected the ratings data before changing the product
packaging and after changing it. Let’s say the Alpha value is 0.05, which indicates the
confidence level is 95%, meaning we are 95% confident about the statistical test results. For
these statistics, we only need to look into the P-value, “P (T<=t) two-tail.” If it is bigger than
0.05, the means are not significantly different. A Two-Sample t-Test, also called an independent
t test, is used to compare the means of two independent groups. To compare three or more
variables, statisticians use an analysis of variance (ANOVA). If the sample size is large, they use
a z-test.
All results of statistical tests are covered by two possibilities: Either the results are significant, or
they aren't. The null hypothesis predicts a non-significant outcome. The alternate hypothesis
predicts significance. Hypothesis testing is something that can be used to make decisions based
on experimental data. It can systematically quantify how certain the result of a statistical
experiment. Most hypothesis testing uses null-hypothesis. The null-hypothesis, denoted H0,
typically proposes a default position, such as if the coin flipping is fair. And it is typically paired
with an alternative hypothesis, such as the coin is biased, denoted H1. Normally, the hypothesis
we care or we want to be true is the null-hypothesis. And the main goal of hypothesis testing is
to tell us whether we have enough evidence to reject the null-hypothesis. For example, “Joey”
might want to test if coin flipping would give a fair result. So he makes an experiment where he
would flip a coin 100 times and let’s say he get results of 52 times for head side and 48 times for
tails side. Would that be fair enough from the statistical view? This is why it’s best to first do a
hypothesis testing.
Khan Academy. (Producer). Hypothesis Testing and P-values [Video File]. Retrieved from
https://www.khanacademy.org/math/probability/statistics-inferential/hypothesistesting/v/hypothesis-testing-and-p-values.
Khan Academy. (Producer). Small Sample Hypothesis Test [Video File]. Retrieved from
https://www.khanacademy.org/math/probability/statistics-inferential/hypothesis-testing/v/smallsample-hypothesis-test.
Khan Academy. (Producer). T-statistic Confidence Interval [Video File]. Retrieved January 24,
2013, from https://www.khanacademy.org/math/probability/statistics-inferential/hypothesistesting/v/t-statistic-confidence-interval.
O’loughlin, E. (2012, November 29). How To Perform a one-way ANOVA Test in Excel 2010
[Video File]. Retrieved from http://www.youtube.com/watch?v=-EV9gn-splM
Tanner, D. E., & Youssef–Morgan, C. M. (2013). Statistics for Managers. San Diego, CA:
Bridgepoint Education, Inc. This text is a Constellation™ course digital materials (CDM) title.