In: Statistics and Probability

A t-test is used to compare the means of one variable for two groups of cases. As an example, a practical application would be to find out the effect of a new drug on blood pressure. Patients with high blood pressure are randomly assigned into two groups, a placebo group and a treatment group. The placebo group would receive conventional treatment while the treatment group would receive a new drug that is expected to lower blood pressure. After treatment for a couple of months, the two sample t-test is used to compare the average blood pressure of the two groups. Below are the results. Determine the alpha value. Complete all five steps for hypothesis test. Conduct and interpret a 99% confidence interval. Sample size for placebo group 120, Sample size for treatment group 120 sample mean for placebo group 127 sample mean for treatment group 125 sample standard deviation for placebo group 4.5 sample standard deviation for treatment group 5.5

**Hypothesis test**-

We have two perform **two sample t-test**.

Suppose, random variables X and Y denote blood pressure for placebo and treatment groups respectively.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Degrees of freedom

Level of significance

Corresponding
[Using R-code
'**1-pt(3.08301,238)+pt(-3.08301,238)**']

We reject our null hypothesis if .

Here we observe that .

So, we reject our null hypothesis.

Hence, based on the given information we can conclude that
**blood pressure of placebo and treatment groups are not
same**.

**99% confidence interval**-

For degrees of freedom 238 we have,

So, 99% confidence interval is given by **(-1.684486,
1.684486)**.

It implies that if blood pressure in placebo and treatment groups are not significantly different, then if we take 100 different pairs of samples, on average in 99 times the difference of average blood pressure of two groups will lie in the interval (-1.684486, 1.684486).

The Independent Samples t Test can only compare the means for
two (and only two) groups. It cannot make comparisons among more
than two groups. If you wish to compare the means across more than
two groups, you will likely want to run an ANOVA.
What is the main differences between an unpaired and paired t-test?
Why would you want to limit the number of variables you are
comparing? Why would you want to start with two groups and work...

The Independent Samples t-Test compares the means of two
independent groups to determine whether there is statistical
evidence that the associated population means are significantly
different. The Independent Samples t-Test is a parametric test.
Give an example of two variables you would compare, what your
theory is and the hypothesis, and how you would find the
independent samples t-test in SPSS.

Provide examples of how the t test and ANOVA could be
used to compare means within your work environment or domain of
interest. Discuss the appropriateness of using the t test
versus ANOVA.

Provide examples of how the t test and ANOVA could be used to
compare means within your work environment or domain of interest.
Discuss the appropriateness of using the t test versus ANOVA.

Provide examples of how the t test and ANOVA could be
used to compare means within your work environment or domain of
interest. Discuss the appropriateness of using the t test
versus ANOVA.

The two-sample t-test is applied to compare whether the average
difference between two groups is significant or if it is due
instead to random chance.
Use good references,
1. Briefly, describe the difference between
Unpaired Two-Sample T-test and
Paired Two-Sample T-test.
2. Provide an application example for Unpaired
Two-Sample T-test, and stablish the Ho and Ha Hypotheses.
3. Provide an application example for Paired
Two-Sample T-test, and stablish the Ho and Ha Hypotheses.
4. Explain the purpose of P-values and...

There are three (3) cases for handling
the comparison of means using the Student’s t-test. For
each of the scenarios listed below, identify which case
(i.e. Case #1, #2, or #3) you would use
in order to determine if the results agree “within experimental
error”: Provide a brief explanation to receive full
credit!
A FDA scientist is testing a sample of ground beef, suspected
of being contaminated with E-Coli, using one of their standard
methods. The average of several replicated...

Generally, we compare two independent sample means via
independent two-sample t test. Is it possible to compare two
independent sample means using ANOVA? please give me a
different answer/ explanation. I know someone already asked about
this question here, please don't copy it and give me the same
answer. THANKS.

In which of the following scenarios will conducting a two-sample
t t -test for means be appropriate? CHECK ALL THAT APPLY. A. To
test if there is a difference between the mean annual income of
husbands and that of wives in Canada. B. To test if the mean annual
income of Ontarians is higher than that of British Columbians. C.
To test if there is a difference between the mean annual income of
male British Columbians and that of female...

5. TWO (INDEPENDENT) SAMPLE T-TEST
(a) Describe the independent samples t-test for two means
briefly. How does it do it? (b) State the null and the alternative
hypothesis. (c) State the assumptions. (d) State the formula for
the test statistic. (e) State the rejection rule with (How to
reject the null hypothesis) (f) Give an real life example of how we
can use the independent samples t-test for two means.

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