Download Carrying out Significance Tests

Carrying out Significance
Tests
Chapter 10
Section 2
What signs to use When writing Null and
Alternate Hypothesis:
• (For our level we use: )
• For Null Hypothesis it is always
• We always set the parameter of interest ________ to
what is _________ to be true
• For Alternate Hypothesis we use
• We set say the parameter is _____________ from what is
___________ to be true.
Which of these could be possible hypotheses
for a significance test?
A
H 0 : p  0.5
B
H a : p  0.5
C
H 0 : p  0.5
H a : p  0.5
H 0 : p  0.5
H a : p  0.5
D
H 0 : p  0.5
H a : p  0.5
Write the Null and Alternate Hypothesis for
the following
• You’ve been using the Random Digit Table all year,
but one day you decided to check out its
randomness. You count the number of times the
digit “9” occurs in the last four rows of the table
and find that there are only 12 “9”’s in the last 160
digits. You suspect that the table is flawed by
having fewer “9”’s then it should and decided to do
a significance test.
Write the Null and Alternate Hypothesis for
the following
• The White House Press secretary comments that
the president currently has a 72% favorable job
approval rating. A pollster challenges this claim as
being too high. His polling service has just
conducted a random survey of 1000 people (calling
both landline and cell phone numbers) and 660
people gave the president a favorable job approval
rating. Do we have reason to doubt the press
secretary?
Write the Null and Alternate Hypothesis for
the following
• A 2009 nationwide random survey of 1500 adults
asked the open-ended question, “What do you
think is the most important problems facing this
country today?” Sixty-nine percent responded with
some form of economic problems (such as economy
in general, unemployment/jobs, etc). Do these data
provide good evidence that more than 2/3 of all
adults believe that economic problems is the most
important problem facing this country today?
Write the Null and Alternate Hypothesis for
the following
• If a die is fair, then the number 5 should occur 1/6
of the time. You have a die that you suspect is
loaded so that the number 5 lands face up more
often then expected. You roll the die 200 times and
get 44 5’s. Do we have evidence that the die is
unfair (i.e. loaded)?
Write the Null and Alternate Hypothesis for
the following
•According to the 2000 U.S. Census, 80.4% of
all U.S. residents 25 years old or older have at
least a high school diploma. In 2005, a
random sample of 3,000 residents 25 years
old or older found that 2,365 had at least a
high school diploma. Is there evidence to
suggest that the number of high school
graduates is lower that reported in the
Census?
Bad Physics Teacher?
• The head of the physics department has found over the
years, students in the final exam average 70% with a
standard deviation of 6.3%. One of his instructors
seems to have a greater number of failures is his classes
so the department head decides to do a hypothesis test.
He takes SRS of 20 final exams from that teacher and
finds that the average score is 67.3%. If there evidence
at the 5% level that this teacher’s students have done
worse that the general population of physics students?
P-values
• The p-value tells us the ______________ we would
get _______ if m is the mean of the population.
• The p-value ______ ________tell us the probability
of getting that result.
Choosing a Level Of Significance (alpha Level)
• How small a p-value is strong evidence against the Null
Hypothesis?
• TWO MAIN THINGS TO CONSIDER…
• How ____________ is H0? If Ho represents an
assumption that has been believed for years, __________
_____________will be needed to persuade
• What are the ________________ of rejecting H0? If
rejecting H0 means that an ______________ changeover
from one type of manufacturing to another  strong
evidence
Choosing a Level of Significance
• THERE IS NO SHARP BORDER BETWEEN “STATISTICALLY
SIGNIFICANT” AND “STATISTICALLY INSIGNIFICANT”, ONLY
INCREASINGLY STRONG EVIDENCE AS THE P-VALUE
DECREASES
• ______ _________treat .05 as the magic level!!!
• A p = .051 or p = .049 does not provide strong evidence. A
____________ ___________ _________may be necessary
to determine significance.
General Cautions
• Look carefully at the __________ data, as well as the
__________ of a statistical test!
• Consider that there _______ _____an effect from a
treatment even if a finding ________ statistically significant;
and, vice versa, there ______ _______be an effect even if a
finding is statistically significant.
• Design a study so that it has a high probability of finding a
real effect.
General Cautions
• Design a study in such a way that the statistics
used to analyze the study are ___________
• No “__________ in, ___________ out” data
• Make sure surveys or experiments are not
________ designed
• Understand that the use of probability in
statistical inference is based on the assumption
that our data is _________ ___________from
the population of interest.
General Cautions
• Be sure that all the data is represented in the
analysis so that “__________” don’t have an
influence in the findings.
• Remember that a significance level of _____ means
that you will get a _______________ finding one
time out of 20 simply due to chance variation. If
you run enough tests, you will get significant
findings ________of the time even if nothing is
going on.
• A confidence interval estimates the ______ of an
effect rather than simply asking if it is too large to
reasonably occur by chance alone.
Identify the null hypothesis, the alternative
hypothesis, and test statistic
•The health of employees is monitored by
periodically weighing them in. A sample of 54
employees has a mean weight of 183.9 lb.
Assuming that σ is known to be 12.2 lb, use a
0.10 significance level to test the claim that the
population mean of all such employees
weights is less than 200 lb.
Identify the null hypothesis, the alternative
hypothesis, and test statistic
•A random sample of 100 pumpkins is
obtained and the mean circumference is
found to be 40.5 cm. Assuming that the
population standard deviation is known
to be 1.6 cm, use a 0.05 significance level
to test the claim that the mean
circumference of all pumpkins is equal to
39.9 cm.
Example 1
•A company wishes to determine if the
average salary of its clerks is less than
the $340 believed by HR. The company
researcher takes a sample of 64 clerks
and finds that =$300 and s = $80. Test
at 5% significance level.
Example 2
•A researcher claims that 10 year olds watch
6.6 hours of TV daily with a standard
deviation of 2.5 hours. You try to verify this
with the following sample data. A SRS of 100
10 year olds have a mean of 6.1 hours. Test
the researcher claim at a 1% significance
level.
Example 3
• An insurance company is reviewing its current
policy rates. When originally setting the rates they
believed that the average claim amount was $1,800.
They are concerned that the true mean is actually
higher than this, because they could potentially lose
a lot of money. They randomly select 40 claims, and
calculate a sample mean of $1,950. Assuming that
the standard deviation of claims is $500, and set a=
05, test to see if the insurance company should be
concerned.
Example
• A random number generator is supposed to
produce random numbers that are uniformly
distributed on the interval of 0 to 1. If this is
true, the numbers generated come from a
population with μ=0.5 and σ =0.2887. A
command to generate 100 random numbers
gives outcomes with mean x =0.4365. Assume
that that the population σ remains fixed. We
want to test
•
Ho: μ=0.5
Ha: μ≠0.5
• Is the result significant at the 5% level?
• Is the result significant at the 1% level?
Confidence Intervals and hypothesis Testing
• Confidence intervals can be used for 2 sided tests.
• You look for Ho to be in the _________.
• If it is you _________________the Ho.
• If not you __________________ the Ho.