Probability Question:
A roulette wheel has 18 red number, 18 black numbers, and 2 green numbers.
If you bet on red, what is the probability of winning?
What is the complement of winning more than half of 20 bets is?
If you place 20 bets on red, what is the probability of winning exactly half of them?
If you place 20 bets on red, what is the probability of winning more than half of them?
All of the rest of this handout uses the following
We’re measuring the size of chocolate kisses. They’re supposed to be 5 grams.
Sample 1 of Kisses:
5.07
5.01
5.02
5.02
4.98
5.03
5.00
4.99
4.87
5.08
What is a 98% confidence interval for the population mean using Sample 1?
What is the margin of error?
Conduct hypothesis test as to whether the mean weight of a kiss is 5 grams.
The null hypothesis is:
The alternative hypothesis is:
Which distribution is being used?
Use α=.01. What is the critical value(s) for the hypothesis test?
What is the test statistic for the hypothesis?
What is the conclusion? State the conclusion in English.
Chapter 11: Two Sample, testing differences in means.
A new kiss making machine is purchased that makes kisses faster. Sample mean from the new
machine is drawn. Assumption: the two samples are INDEPENDENT
Sample 2 of Kisses:
5.06
4.99
5.03
5.00
4.96
5.04
5.00
4.96
4.88
5.06
What a 98% confidence interval for the difference in population means using the two samples?
What is the margin of error?
Conduct hypothesis test as to whether the mean weight of a kiss from the new machine is different
from the old machine.
The null hypothesis is:
The alternative hypothesis is:
Which distribution is being used?
Use α=.01. What is the critical value(s) for the hypothesis test?
What is the test statistic for the hypothesis?
What is the conclusion?
Each sample above is drawn from a different nozzle that produces kisses, thus the samples are
paired and not independent.
What is the mean difference?
Testing Difference in Means, Paired Sample (Non-independent)
What if you have two samples, but the data is paired. That is, observation 1 in sample 1 goes with
observation 1 in sample 2?
What are some potential examples of this?
Assume the two samples above (kisses example) are paired.
Calculate the difference between the two samples.
The null hypothesis is:
The alternative hypothesis is:
Which distribution is being used?
Use α=.01. What is the critical value(s) for the hypothesis test?
What is the test statistic for the hypothesis?
What is the conclusion?
Regression (review)
A company does a marketing study by selling a product at 10 different stores at 10 different prices.
Below presents their results.
Find the Least Squares Regression Line: Qty = b0 + b1Price
You’re regressing what on what?
State : R2, and calculate the Predicted Qty and the Residual
Interpret b1
Interpret the Y intercept
Find the X intercept and interpret that
If the price rises by $2, predict what happens to sales
If the company set a price of $10.75, what would be the predicted sales?
Do a hypothesis test on whether higher prices reduce quantity sold.
Store
1
2
3
4
5
6
7
8
9
10
Price (X)
$7
9.50
8
11.5
10
10.5
11
9
7.5
8.5
Qty Sold (Y)
335
248
291
195
255
237
229
294
302
277
Pred Qty
Resid
2 
(n  1) s 2
 02
Hypothesis Test, Standard Deviation (Section 9.5)
After enactment of new financial laws, financial economists are curious if the laws have changed
the risk of the stock market. Risk is commonly measured by the standard deviation. Assume stock
returns are normally distributed (not a proper assumption) and independent. Prior to the passage of
the new laws, the standard deviation of stocks were .27. After the passage of the laws, a sample of
20 returns were tracked. The sample standard deviation was .24. Has the standard deviation
changed?
State the null hypothesis
State the alternative hypothesis
Is this a one tail or two tail? If one tail, which?
Which distribution is being used?
Assume α = .05. What are the critical values?
2 
(n  1) s 2
 02
What is the value of the test statistic?
What conclusion do you draw?
Example 2 of Testing Standard Deviation
A new corn hybrid is created. The old corn crop had a mean of 23 grams and standard deviation of
.2 grams. A sample of 10 ears of corn are weighed. Conduct a hypothesis test to determine if the
variation in weight has changed. Weight of sample: 24.36, 23.54, 24.18, 24.06, 23.74, 23.92,
24.06, 24.72, 24.56, 23.70.