Interval Estimation and Hypothesis Testing Procedures
Note:
a. When the standard deviation of the population “” is known use Z
(normal) distribution.
b. When standard deviation of the population “” unknown use the
standard deviation of the sample ”S” and the t distribution.
I.
Interval Estimation Procedure:
Interval Estimate = Sample Statistic  (Z or t)(Standard Error)
II. Hypothesis Testing Procedure:
Step 1:
Develop the null and the alternative hypotheses.
Step 2:
Specify the level of significance.
Step 3:
Compute the test statistic (t or Z) from the sample data.
Test Statistic 
Sample
Statistic   Hypothesiz ed Population Parameter 
Standard Error
Rejection Rule: p-Value Approach
Step 4:
Compute the p-value by using the test statistic (t or Z) from step 3.
Step 5:
Reject Ho if p-value .
Rejection Rule: Critical Value Approach
Step 4:
Determine the critical value(s) of t or Z at the specified level of significance  and
set up the rejection rule.
Step 5:
Compare the test statistic from step 3 to that of the critical value(s) from step 4. If
the test statistic is beyond the critical value(s), reject the null hypothesis.
Review Problems for Chapters 8 and 9
Interval Estimation and Hypothesis Testing
I.
Means
1. The Standard Deviation of the population  is known.
Chattanooga Paper Company makes various types of paper products. One of their products is a
30 mils thick paper. In order to ensure that the thickness of the paper meets the 30 mils
specification, random cuts of paper are selected and the thickness of each cut is measured. A
sample of 256 cuts had a mean thickness of 30.3 mils. From past information it is known that
the standard deviation of the population  is known to be 4 mils.
a. Develop a 95% confidence for the thickness of the paper.
b. The company considers the production in control if the thickness does not deviate from
the desired 30 mils by more than + 3%. Is the production in control? Explain.
c. At 95% confidence, test to see if the mean thickness is significantly more than 30 mils.
d. Compute the p-value and interpret its meaning.
Professor Ahmadi’s lecture notes 2
2. The Standard Deviation of the population  is unknown.
The cost of a roll of camera film (35 mm, 24 exposure) in a sample of 12 cities worldwide is
shown below.
City
Rio de Janeiro
Stockholm
Tokyo
Moscow
Paris
London
New York
Mexico City
Sydney
Honolulu
Cairo
Hong Kong
Cost (in dollars)
12.14
7.47
6.56
5.69
5.62
5.41
4.33
4.00
3.62
3.43
3.40
2.73
a. Using Excel, compute the basic descriptive statistics (the mean, the median, the mode,
the standard deviation, and the standard error of the mean) for the cost of film.
b. Determine a 95% confidence interval for the population mean.
c. At 95% confidence test to determine if the average price is significantly different from
$3.50?
d. Estimate the p-value and explain its meaning.
Professor Ahmadi’s lecture notes 3
II.
Proportions
3. In a random sample of 400 employees of a local company 180 were female.
a. At 95% confidence determine if the proportion of females in the company is significantly
less than 50%.
b. Compute the p-value and explain its meaning.
4. Many people who bought Xbox gaming systems, have complained about having received
defective systems. In a sample of 1200 units sold, 18 units were defective.
a. Determine a 95% confidence interval for the percentage of defective systems.
b. If 1.5 million Xboxes were sold, determine an interval for the number of defectives.
c. At 95% confidence, test to see if the percentage of defective systems produced by Xbox
has exceeded the industry standard. The industry standard for such systems has been 99
percent non-defective systems
d. Compute the p-value and interpret its meaning.
Professor Ahmadi’s lecture notes 4
Reading the “t” and the “Z” values
For each of the following, read the t statistic from the table and write its value in the space
provided.
1. A Two-Tailed Test, a sample of 29 at 80% confidence t =
?
2. A One-Tailed Test (upper tail), a sample size of 26 at 90% confidence t =
?
3. A One-Tailed Test (lower tail), a sample size of 22 at 95% confidence t =
?
For each of the following, read the Z statistic from the table and write its value in the space
provided.
4. A Two-Tailed Test at 98.4% confidence Z =
?
5. A One-Tailed Test (lower tail) at 89.8% confidence Z =
?
6. A One-Tailed Test (upper tail) at 93.7% confidence Z =
?
Professor Ahmadi’s lecture notes 5
Your Turn
1. A random sample of 64 SAT scores of students applying for merit scholarships showed an
average of 1400 with a sample standard deviation of 240. Provide a 95% confidence interval for
the SAT scores of all the students who applied for the merit scholarships.
2. In the last presidential election, a sample of 800 registered voters in California showed that
200 of them voted for the incumbent president. Develop a 95% confidence interval estimate for
the proportion of all California registered voters who voted for the incumbent president.
3.
From a population of cereal boxes marked "12 ounces," a sample of 64 boxes is selected
and the content of each box is weighed. The sample revealed a mean of 11.7 ounces with a
standard deviation of 1.6 ounces.
a. Using the critical value approach, test to see if the mean of the population is significantly
less 12 ounces. Use a 0.05 level of significance.
b. Using the p-value approach, test to see if the mean of the population is significantly less
than 12 ounces. Use a 0.05 level of significance.
Professor Ahmadi’s lecture notes 6