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
Do the above test again, but this time test whether stocks have become less risky
Example 3 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.
A company does a marketing study by selling a product at 10 different stores at 10 different prices.
Plot the above data below.
Find the Least Squares Regression Line: Qty = a + b Price
Draw the Least Square Regression Line on the graph below
State r, R2, and calculate the Predicted Qty and the Residual
Interpret b1, Y intercept, X intercept
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?
If the company wants to sell 275 goods, what price should they charge?
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
Demand
360
340
Quantity Sold
320
300
280
260
240
220
200
6
7
8
9
Price
10
11
12
Review, Confidence Interval and Hypothesis Test
A sample of how much people watch TV was conducted. The numbers represent the
number of hours the person watched per day.
Data Set: 2, 4.5, 7, 1, 2.5, 4, 2, 2.5, 3, 3.5, 2.5, 5.5, 0
a. What must be true to draw inferences from the data? Test this with a modified box
plot.
b. Construct a 95% confidence interval for the population mean.
c. What is the margin of error?
d. What does it mean that you are 95% confident in that interval?
Conduct a hypothesis test to see if people watch less than 4.5 hours of TV per day. Level of
significance is .05
e. State the null and alternative hypothesis
f. Using the critical value method, what is/are the critical value(s), and which
distribution is being used?
g. Using the critical value method, what is the result (statistically) of the hypothesis test
and why?
h. Draw a diagram to represent the previous test.
i. Using the P-value method, what is the result (statistically) of the hypothesis test and
why?
j. State, in English, the result of the hypothesis test.