Question

The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. Select an application of the two-sample t-test and describe how it was justified to use the t-test for this particular application. Describe what the P-value of the 2-sample t-test of your example in part (1) means. Note that you are not being asked to provide a general definition of the P-value in hypothesis testing problems. You are being asked to interpret the P-value in the context of the particular example that you have selected.

Answer #1

A2 sample t test can be used when we think that variances of both population 1 and population 2 are about the same and can be said to be similar

An application of the 2 sample t test is comparing 2 machines of the same unit

one machine can be new relative to the other but both are doing the same task

To test if the new machine is actually doing the task faster than the old machine we can use a 2 sample t test

At a said level of significance we can check the null hypothesis and alternate hypothesis and confirm if we need to reject the null or not

True or False: For all hypothesis tests, a small p-value means
we will reject the null.
True or False: If you are testing the means of two groups, then
you would use ANOVA.
True or False: A two-sample confidence interval must capture
zero to show the groups are different.
True or False: The test statistic for ANOVA is the
f-statistic.
True or False: For Chi-Square tests, if the observed counts and
expected counts are extremely different, then we would have...

Which testing method—one-sample or two-sample parameter tests—is
the better test to use to formulate an answer to a hypothesis

The commonly used critical Z values are 1.645 for a 90%
confidence interval (or 2-tailed, .10 level of significance), 1.96
for 95% confidence and 2.58 for 99% confidence. If a different
confidence level is required, such as 92%, how can you determine
the critical Z value?
What is the relationship between the confidence level and the
level of significance of a 2-tail test?
Which Hypothesis Tests use Z distributions?
Which Hypothesis Tests use a Student’s t distribution?
Which Hypotheses Tests...

The one sample t-test from a sample of n = 19 observations for
the two-sided (two-tailed) test of
H0: μ = 6
H1: μ ≠ 6
Has a t test statistic value = 1.93. You may assume that the
original population from which the sample was taken is symmetric
and fairly Normal.
Computer output for a t test:
One-Sample T: Test of mu = 6 vs not = 6
N Mean
StDev SE Mean 95%
CI
T P
19 6.200 ...

Hypothesis testing is the basis of inferential statistics.
Statisticians are always coming up with new tests and testing new
characteristics of population parameters. One of the simplest tests
that currently exist is the one-sample test for means.
A random sample is drawn. If the population variance is known,
then we use the Z test; if the population variance is unknown, we
use the T test. In addition, there are some additional assumptions
that can be made. For example, if a...

For all hypothesis tests, be sure to include information
for all 7 steps. For any two-sample or paired t-tests that you
perform, in Step 6, show the decision rule based on BOTH the
critical value and the p-value. Use the online app for the
t-distribution to compute your p-values.
1. Cortisol level determinations were made on
two samples of women at childbirth. Group 1 subjects underwent
emergency cesarean section following induced labor. Group 2
subjects delivered by either cesarean section...

We are studying One Sample tests of Hypothesis. My
problem/"story" reads as: From the class surveys, a facilitator
finds that 68 of 98 students who have taken a particular math
course were born in AZ. The college is interested in determining if
people who were born Outside of AZ need to be targeted for a
marketing campaign. Analyze this information using the five step
hypothesis testing process to test the claim that greater than 60%
of ASU students were born...

Question 3: Hypothesis Testing - One-Sided Test Boston Co.
Cereal, Inc., has asked you to study the variability of the weights
of cereal bags produced in their plant located in rural Indonesia.
The package weights are known to be normally distributed with the
variance of 50. Using a random sample of n=71, you find that the
sample mean weight is 40. The marketing vice president claims that
there is a very small chance that the population means weight is
less...

For each of the following two-samples t-tests (problems
1-6): (a) Determine if a F test for the ratio of two variances is
appropriate to calculate for the context. If it is appropriate,
conduct the analysis and report the result. Include what
statistical conclusion you should draw from the analysis (i.e.,
whether you should conduct a pooled-variance t-test or an
unequal-variances t-test). (b) Identify the most appropriate t-test
to conduct for the situation/data given. Don’t forget to consider
if the context...

How do you determine whether or not the paired t test is
appropriate for a two-sample hypothesis? Please give an
example.

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