One of the central questions that Guinness
wanted to understand was which barley would
be the best. From his research, Gossett realized
that differences in the data could be due to
natural variation or accidental in nature.
Gossett also inferred that the resulting
differences could be the product of the
difference in how the barley was treated or
perhaps just due to natural variation. On the
other hand, the anomalies could also be the
result of divergences in how the barley was
treated or processed, which if addressed could
lead to better methods of distillation.
To determine the best barley solution, Gossett
inferred that new statistical methods would
need to determine the answer. He developed
many of the methods that were needed to
answer those questions.
Gossett went on to spend a year at University
College in London during his time while
working at the brewery. He subsequently
published his research under the name of

"
Student
" because Guinness would not allow
him to use his own name. He is known as a
founder of statistical inference, and his work
with small samples came to be known as the
Student t-test
.
Interactive Examples
1
1
What is the critical value for a 92% confidence level?

2
What is the confidence level for a critical value of -1.85?

3
About what portion of observations is covered by ± three standard deviations around the mean?

4
Construct a 96% confidence interval if a sampling distribution has a mean of 20, standard
deviation of 5, and size of 100?

1

What is the critical value for a 92% confidence level?

2
Which of the following is true regarding a confidence interval for the population mean?
Ẋ

3
Which of the following may not be available when constructing a confidence interval?

4
Construct a 96% confidence interval if a sampling distribution has a mean of 10, standard
deviation of 2, and size of 36?

5
About what portion of observations is covered by ± one standard deviation around the mean?

6
Put the steps below in calculation of a confidence interval from left to right.

Find the value of the critical value for the given confidence level
Use the population standard deviation if known, otherwise use the sample standard deviation
Apply the values to the equation for the confidence interval
7
Which of the following factors does a confidence interval depend on?