In this paper I am going to perform a one-tailed, one-sample t¬-test in
order to test the null hypothesis that the average number of ounces of
cereal per box equals sixteen. A manufacturer of a particular brand of
cereal maintains there is an average of sixteen ounces of cereal per
box. On the other hand, a consumer group asserts the average is fewer
than sixteen ounces per box. The consumer group is going to file a
class action lawsuit for false advertising if the average is fewer than
sixteen ounces per box. I was hired by the consumer group to determine
whether the consumer group is correct or the cereal manufacturer is
correct.
According to Sprinthall (2003, p. 249),
…Sometimes, however, a researcher not only assumes that a mean
difference between samples will occur but also predicts the direction
of the difference¬. When this happens, the statistical decision is not
based on both tails of the distribution, but only one. In this
instance, the sign of the t ratio is crucial. When conducted in this
way, the t test is called a one-tail t test. The calculation of a one-
tail t test is identical to that of the two-tail t. The only
differences are in the way the alternative hypothesis is written and in
the method used for looking up the table value of t [italics in
original].
I randomly selected 20 supermarkets, and from each supermarket
I randomly selected one box of the manufacturer’s cereal. I then
weighed the cereal in each box for all twenty boxes. I came up with
numbers ranging from 12.4 being the lowest to 18.4 being the highest
weight of the cereal. I then used the one-tailed, one-sample t test to
test the null hypothesis that the average number of ounces of cereal
per box equals sixteen.
After completing the one-tailed, one-sample t test I compared the alpha
level to the significance and decided to retain the null hypothesis. I
did this because if the significance level were less than the alpha
level then the null hypothesis would be rejected, and if the
significance level is greater than the null hypothesis then the null
hypothesis would be retained. In this example, the significance
is .0605 compared to .05, which is the alpha level. The significance
is much more than the alpha level so, therefore, I retained the null
hypothesis because there is a large probability that it is true. Also,
I found that the null hypothesis should be retained because the mean
average number of ounces of cereal per box (M=15.34, SD= .41) does not
differ significantly from the overall average of ounces of cereal per
box of 20, t(19)= -1.624, p=.0605. The difference is due to chance.
In this example, the manufacturer is correct. It is true that
there is an average of sixteen ounces of cereal per box. So therefore,
the consumer group will not be filing a class action lawsuit against
this specific manufacturer.
References
Sprinthall, R.C. (2003). Basic Statistical Analysis (7th ed.). Boston:
Allyn and Bacon.

Registered Members, login
Join now, it's free

Property of EssaySwap.com