t.notebook
May 05, 2017
t - Distribution
Also called the independent t-test, two sample t-test,
independent samples t-test or student's t-test.
1 sample: used to determine whether a sample of
observations could have been generated by a process with
a specific mean
2 sample: used to determine whether there is a
statistically significant difference between the means in
two unrelated groups.
For 10 students who watched Sesame Street when they
were 4 years old and 10 students who did not watch
Sesame Street when they were 4 years old, was there a
difference in their high school grades?
1. Identify the level of significance
2. Identify the degrees of freedom (n-1)
3. Find the critical values using the t-Distrbution Table
a. left-tailed: use the "One Tail " negative
column
b. right-tailed: use the "One Tail " postive
column
c. two-tailed: use the "Two Tails " with both
positive and negative signs.
On the 1st day, you can wear any of the 7 hats. On the
second day, you can choose from the remaining 6 hats,
on day 3, the remaining 5 hats, and so.
When day 6 rolls around, you still have a choice between
2 hats that you haven't worn that week. But after you
choose your hat for day 6, you have no more choices for
the hat on day 7. You must wear the remaining hat.
You had 7-1=6 days of hat "freedom" - in which you could
vary the choice of hat that you wore.
What is a degree of freedom?
It is the freedom to vary. Forget about statistics.
Imagine you're a fun loving person who loves to wear
hats. You couldn't care less what a degree of freedom
is. You believe variety is the spice of life.
Unfortunately, you have constraints, You only have 7
hats. Yet you want to wear a different hat each day of
the week.
Using the chart:
Find the critical value for a left tailed test with
=0.01 and n=14.
Find the critical value for a right tailed test with
=0.10 and n = 9
Find the critical value for a two-tailed test with
=0.05 and n = 16
1
t.notebook
May 05, 2017
t Test for a Mean
, n< 30,
unknown
The t-test for a mean is a test for a population mean. It
can be used when the populations is normal (or nearly
normal) , is uknown and n < 30. The test statistic is the
sample mean and the standardized test statistic is:
1. State the claim mathematically and verbally.
Identify the null and alternative hypotheses.
2. Specify the level of significance
3. Identify the degrees of freedom
4. Determine the critical values
5. Determine the rejection region.
d.f = n - 1
6. Find the standardized test statistic and sketch
its graph
7. Make a decision to reject or fail to reject the
null hypothesis
An insurance agent says that the mean cost of insuring a 2008
Honda CRV is less than $ 1200. A random sample of 7 similar
insurance quotes has a mean cost of $1125 and a standard
deviation of $55. Is there enough evidence to support the
agent's claim at =0.10? assume the population is normally
distributed
8. Write a statement to interpret the decision in
the context of the original claim
An industrial company claims that the mean pH level of the
water in a nearby river is 6.8. You randomly select 19 water
samples and measure the pH level of each. The sample
mean and standard deviation are 6.7 and 0.24, respectively.
P-values and t Tests
Is there enough evidence to reject the company's claim at
= 0.05? Assume the population is normally distributed.
Another Department of Motor Vehicles office claims
that the mean wait time is at most 18 minutes. A
random sample of 12 people has a mean wait time of 15
minutes with a standard deviation of 2.2 minutes. At
= 0.05, test the office's claim, Assume the
population is normally distributed.
2