STAT E100 Section Week 10 Hypothesis testing, 1- Proportion, 2-
Proportion Z tests, 2- Sample T tests
Slide 2
Course Review - Changing the recorded section time this coming
week, more details to come. - Slides are posted on the website
under > sections > Kelas section - Project guidelines, get
started early! - Its worth 15% of the overall grade. The more time
you have, the more feedback that you can get. - The exams are
graded, see your TA for your midterm exam. - If you did not do as
well as you hoped, remember, the midterm is worth 20%
(undergraduates) or 15% (graduate students). - Exams are
cumulative, about 20% future exams will be old stuff. - Email your
TA to join the study group!
Slide 3
Key Inference Concepts and Equations: Two main inferential
techniques: Confidence Intervals - for estimating values of
population parameters Hypothesis Testing- for deciding whether the
population supports a specific idea/model/hypothesis The results of
the tests should agree!
Slide 4
A test of the null hypothesis H0: = 0 gives a test statistic z
= 1.85. a) What is the p-value if the alternative is HA: > 0 ?
b) What is the p-value if the alternative is HA: < 0 ? c) What
is the p-value if the alternative is HA: 0 ? d) Would the 95%
confidence interval for the true mean contain the value 0 ? Why? e)
Would the 90% confidence interval for the true mean contain the
value 0 ? Why? Homework Review
Slide 5
A large study conducted in 2000 showed that adult men spent an
average of 11 hours a week watching sports on television. A random
sample of 16 adult men this year showed that they now spend an
average of 9 hours a week watching sports on television. The
standard deviation of these 16 values was 3 hours. c) Show how the
test of hypothesis results in part (a) are consistent with the
confidence interval results in part (b). Homework Review
Slide 6
Key Equations: For 1-proportion z- significance: For
1-proportion z- interval: For interval and hypothesis test to be
valid, we need both: np 10 and n(1 p) 10
Slide 7
Key Equations: For 2-proportion z- significance: with pooling:
For 2-proportion Z - interval:
Slide 8
Key Equations: For 2 sample t- significance: For 2 sample t-
interval: In the formula, t* is the value from the t df
distribution, with degrees of freedom df = min(n 1 -1, n 2 -1),
with area between t* and t*.
Slide 9
53% of Harvard Extension School students are female. 121 of the
205 students in Stat E100 are women. Is there evidence that there
is a bias in the students who enroll in Stat E100? Sample Question
#1
Slide 10
53% of Harvard Extension School students are female. 121 of the
205 students in Stat E100 are women. Is there evidence that there
is a bias in the students who enroll in Stat E100? 1-proportion z-
significance test Ho: p 0 = p hat = 0.53 Ha: p 0 p hat = 0.53 Since
p > 0.05, we cannot reject the null hypothesis that the
proportion of female Harvard Extension School students is the same
as the proportion of female Extension School students that enroll
in Stat E100. There is not enough evidence to suggest that there is
a bias in the students that enroll in Stat E100. Sample Question
#1
Slide 11
In 2005-2008 David Ortiz of the Boston Red Sox was lauded for
being a clutch hitter. That is, he batted much better with runners
in scoring position than in all other situations. The data is as
follows: situation outcome | clutch other | Total
---------------+-------------------------+---------- hits | 201 424
| 625 outs | 405 1127 | 1532
---------------+-------------------------+---------- Total | 606
1551 | 2157 a) What proportion of the time did Ortiz get a hit
during clutch situations ( )? What about during the other
situations? Perform a 2-sample proportion test to determine whether
David Ortiz truly is a different hitter in clutch situations.
Sample Question #2
Slide 12
In 2005-2008 David Ortiz of the Boston Red Sox was lauded for
being a clutch hitter. That is, he batted much better with runners
in scoring position than in all other situations. a) What
proportion of the time did Ortiz get a hit during clutch situations
( )? What about during the other situations? Perform a 2-sample
proportion test to determine whether David Ortiz truly is a
different hitter in clutch situations. 2-proportion z- significance
test H o : p 1 - p 2 = 0 H a : p 1 - p 2 0 Since p < 0.05, we
can reject the null hypothesis that David Ortiz truly is not a
different hitter in clutch situations. We have evidence to suggest
that David Ortiz truly is a clutch hitter. Sample Question #2
Slide 13
Is sex related to family size? In a survey of the stat 104
students last year, students were asked to report their sex and
family size (how many children in your family?). Of the 70 female
students, the mean number of children was 2.643 with sd = 1.104. Of
the 41 male students, the mean number of children was 2.366 with sd
= 0.994. Is there statistical evidence to support the claim that
family size of Harvard students is related to sex? Sample Question
#3
Slide 14
Is sex related to family size? In a survey of the stat 104
students last year, students were asked to report their sex and
family size (how many children in your family?). Of the 70 female
students, the mean number of children was 2.643 with sd = 1.104. Of
the 41 male students, the mean number of children was 2.366 with sd
= 0.994. Is there statistical evidence to support the claim that
family size of Harvard students is related to sex? 2- sided t-
significance test H o : f - m = 0 H a : f - m 0 Since p > 0.05,
we cannot reject the null hypothesis that there is no relationship
between family size and sex. We do not have evidence to support the
claim that family size of Harvard students is related to sex.
Sample Question #3