SAMPLE MIDTERM EXAM
STAT 53-10 Spring 2006
Answer all the questions. Please show full work for partial credit.
1) Consider the following data on the number of hits to a Library website on 14 randomly picked days: 390 406 446 420 370 328 410 320 368
HW is due in discussion Nov 8th.
Two-sided test for
H0: = 0 vs
The alternative hypothesis is called a two-sided alternative.
Idea: for testing H0: = 0 vs. Ha: 0 we reject H0 (and favor the
alternative Ha) if the sample mean xis either much larger
OVERVIEW of what we learned about the normal:
If X is a normal rv with mean and sd , then
(X -)/ is standard normal and can be denoted by Z, i.e. Z= (X
-)/ is a standard normal random variable (rv).
IMPORTANT: get into the habit of sketching norma
The quiz on Tuesday (9/20) will be on random variables, expected
value, variance and standard deviation, roughly sections 4.1-4.3. I
will post an announcement about it on Blackboard.
Recap of discrete random variables (Ch 4)
Informally, can think of a dis
Remember- HW for credit due online check back on
Also check your e-mail.
Next weeks quiz will be on small-sample CI for (in class
Section 9.2 (through end of p 437, and also the second blue box
Conditions Required on p 438)
Remember, there is HW due Nov 22nd, Tuesday before
Thanksgiving. There is no quiz Nov 22nd, and no lecture.
There will be a quiz on Nov 29th.
Today we finish hypothesis testing.
I will also introduce a new topic regression.
Weve covered the large sample t
Probabilitynew topic from Chapter 3
READING ASSIGNMENT: SECTIONS 3.1-3.4
The object of statistical inference is to say something about the
population given a (random) sample.
To carry out statistical inference, we need to calculate probabilities.
I will post announcement on Blackboard about next weeks quiz on
CIs (Confidence Intervals) for and p.
Formula for large-sample CI for (Section 7.2)
100(1- )% CI for is
(X- z /2 x , X+ z /2 x ),
where z /2 is a value from the Z-table, X is the sampl
We started Ch. 11.
Using data set (xi , yi ), i=1,2,.,n we calculated the
LS (least squares) regression equation
Y = ^0 + ^1 X , where the slope and intercept were calculated
from the data. (p 592)
We assumed a model for the data
Y = 0 + 1 X + ,
For the sample mean for a sample of size n from a population with mean
and standard deviation ,
x = / (n)
The Central Limit Theorem (CLT) also tells us that for large n, the
sample mean has (approximately) a normal distribution.
The university has scheduled the final for Tues, Dec 20th, at 3pm.
Small-sample test of hypotheses about population mean (Section
We came across t distributions in small-sample confidence
intervals (CI) for .
Suppose that n is small (Central Limit th
There will be a quiz in discussion on Tuesday 11/29, after
New topic Regression and correlation (Ch 11)
Regression: find the connection between two variables X, Y from a
data set and use X to predict Y.
Start with data set (xi , yi ), i=1,2,
The next quiz (in discussion Tuesday) will be on probability.
Practice problems will be posted on Blackboard.
A U B the union of two events A and B
A B the intersection of two events A and B
Acthe complement of A
Rule of complements
The next HW will be due in discussion Tuesday, November 8th.
Check Blackboard for an announcement.
Tests of hypotheses another form of inference (Ch 8)
Competing statements (hypotheses) about a population mean: calories
per serving of a snack advertised a
The temperature is 88someone says its unusually hot.
Do you agree?
What criterion88 is unusually high for this time of day
and this day of year?
- What does that mean?
Comparative statement is temperature high compared to
Today, we will talk about independence of events (sec 3.6),
review probability, and move on to discrete random variables
The latter will be on next weeks quiz.
Events A and B are independent events if the occurrence of B does
Quiz Tuesday 10/4 on continuous random variables and the normal
distribution. Ch 5, sections 5.1, 5.3
Free peer tutoring is available in the Department of Statistics,
Rome Hall 7th floor.
A normal distribution with mean and sd can be converted
The quiz on Oct 11th will be on normal approximations, sections 5.5, 6.1,
6.3I will post practice exercises.
Vital fact about a sample statistic it is a random quantity that can vary
from sample to sample. Thus one can think of its probability
m. RA v2: KA LPATH y
Mob 2?, 2008
Circle your section & TAs- [email protected] 37 38 39 TA: Rick Ravi
[Show the steps in your work- It Is not enough just to write down an answer without
showing the calculations or expiaining how you got the answ
There is no discussion Tuesday 10/25 (Fall Break).
I will post on Blackboard how/when to submit HW 2.
I will also post an announcement about the next quiz.
Today well cover the small sample CI for .
Section 7.3 (small sample CI for )read it
Suppose that n
Next weeks quiz in discussion will be on the binomial.
The standard example of a binomial rv is the number of heads in n
tosses of a coin. The tosses are independent, and the probability of
head is the same for each toss.
We worked through an example with
There will be a quiz next Tuesday announcement will be posted
I will also post the HW that will be due Tuesday, Nov 22nd.
Hypothesis tests for difference of population means
Large, independent samples
Section 9.2, pp 438-439. Just after the