You conduct a survey of a sample of 25 members of this year’s graduating business
students and find that the average GPA is 3.2. The standard deviation of the sample is 0.4.
Over the last 10 years, the average GPA has been 3.0. Is the GPA of this year’s students
significantly different from the long-run average?
When looking at this situation one can think that the hypothesis has almost no significant
difference between the survey and the data collected in the past 10 years. Basically, there is a
null hypothesis, and any differences would just be experimental. Testing a null hypothesis is an
important step. “In science, "proving" something doesn't occur. Science uses math to determine
the probability a statement is true or false. It turns out it's much easier to disprove a hypothesis
than to ever prove one.” (Halmenstine, 2018 p. NA) Ultimately, the difference of long-term
average of 3.0 GPA and the current survey average GPA of 3.2 is due to sampling variations.
The decision here is finding out if a sampling variation, in this case, could go as far as 0.2. A
parametric test would be a great way to figure out if the difference is significant. In order to
calculate the value, there are a few steps needed in the parametric test. By using the t-test the
calculated value is 2.50. Using the Table-C, the degrees of freedom is 24, thus the critical value
is 1.711 wit alpha being 0.05. With all of this presented, the calculated value being greater than
the critical value helps us conclude that the null hypothesis is rejected. This calculated value
shows that the survey from this year is significantly different from the 10-year average.
At what alpha level would it be significant?
“The alpha-level specifies our attitude to the analysis. We use the value of alpha to
characterize our approach to the decision problem.” (Wheeler, 2014, p.NA) In order to find out
what level alpha would be significant the textbook is needed to be referenced. The turning point
for alpha is 0.0197, with the critical value being 2.492. At those levels the reference point
becomes significant. Anything above this value, like the example above, the student’s GPA are
not significantly different. However, anything blow is significantly different.
References
Helmenstine, A. M. (2018, May 20). What Is a Null Hypothesis? Definition and Examples.
Retrieved from https://www.thoughtco.com/definition-of-null-hypothesis-and-examples-
605436
Wheeler, Donald. (2014, June) Quality Digest: What Is an Alpha-Level? Retrieved from
https://www.qualitydigest.com/inside/quality-insider-column/what-alpha-level.html.
You contact a random sample of 36 graduates of Western University and learn that their
starting salaries averaged $28,000 last year. You then contact a random sample of 40
graduates from Eastern University and find that their average starting salary was
$28,800. In each case, the standard deviation of the sample was $1,000.
a Test the null hypothesis that there is no difference between average salaries received
by the graduates of the two schools.
In order to test the null hypothesis, it is important to fully understand the terms and
process. The null hypothesis in this case is that there is no difference at all between the average
salaries received at the two universities. What we know is that Eastern University students
received a higher salary than Western University by an average of $800. Now, the fact that
Eastern University students receive a higher salary is the alternative hypothesis. The proper test
for this situation, the best way to test the null hypothesis, is the t-test. Like discussion question
14.7, the significance level was chosen for alpha at 0.05. Using this, the test produces a
calculated value of 3.436. The critical value comes out to be 1.66. It is easy to see here that the
calculated value is much higher than the critical value. This means that the null hypothesis
should be rejected. Therefore, that concludes that the students from Eastern University received
a higher annual starting salary.
b What assumptions are necessary for this test?
“The first assumption made regarding t-tests concerns the scale of measurement. The
assumption for a t-test 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.” (Maverick, 2018, p. NA) Certain
assumptions are needed for the t-test to work. For one, having random samples that all come
from normal populations. The is to have it come from the same variance as well. “A random
sample is a sample that is chosen randomly. It could be more accurately called a randomly
chosen sample. Random samples are used to avoid bias and other unwanted effects.” (Hood,
2018, p. NA) This is needed because it increases accuracy and allows an equal chance each time.
When the deviations of sample are equal, or close to equal, the variance is a critical assumption
for the t-test. These assumptions are needed for the test to conducted correctly.
References
Hood, S. (2018, August 14). Simple Random Sample: Definition and Examples. Retrieved from
https://www.statisticshowto.datasciencecentral.com/simple-random-sample/
Maverick, J. (2018, March 25). What assumptions are made when conducting a t-test? Retrieved
from https://www.investopedia.com/ask/answers/073115/what-assumptions-are-made-
when-conducting-ttest.asp
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