Revision Class 1: In Class Examples
Example 1: EPA ratings (this example is associated with slides 3 to 8).
The EPA calculate car mileage for all cars currently in the US market. You wish to analyze these
data in Microsoft Excel. Load the EPAGAS.xlsx work
Revision Class 2: In Class Examples
All of the hand calculations that are included as part of this course can be implemented in
Microsoft Excel. In fact, Excel is much more accurate than using a combination of hand
calculations and tables. However, it is
Revision Class 3: In Class Examples
Board Example 1: Black Friday shopping
Fill in the remaining steps
95% Confidence Interval
x z / 2 x
x + z / 2 x
In Microsoft Excel
Ill demonstrate two ways of doing this: The first is using basic functions and mirror
D. BRIAN BLANK, PH.D.
VISITING ASSISTANT PROFESSOR OF FINANCE
SPRING SEMESTER 2017
1. Which of the following is the difference between a firm's current assets and liabilities?
Lab Assignment 3
Due: 2/15, Wednesday
Use SPSS program to do the following problems
1. (2.5 pts) A person wanted to compare the battery life of subcompact cameras and compact cameras.
The following table shows the samples the person selected.
7. 3 Exercise 1 A survey wants to compare male and female shoppers in a
metropolitan area. Among the questions asked was, Do you enjoy shopping for
clothing? Of 260 females, 224 answered yes. Of 240 males, 136 answered yes.
(a) What are the populations?
7.2 Exercise 1 A person wants to compare the prices of two rental companies
Thrifty and Hertz. The following data represent the rental price on a day for a
compact automobile charged by the two companies in 3 locations.
Lab Assignment 1
Due: 2/1, Wednesday
Use SPSS to do the following problems.
For each problem: (i) Provide output (ii) Draw conclusion based on the output.
1. (2.5 pts) A person wants to estimate the annual expenditure on apparel and services
Lab Assignment 2
Due: 2/8, Wednesday
Do problems 1 5 using Excel program.
1. (1.5 pts) A person wants to estimate the mean customer waiting time of a bank. A sample 15
customers is randomly selected and the waiting times are as follows:
Project 1 Assignment
Due: 3/1, Wednesday
The statistical method can be one of the following:
Confidence intervals (Chapter 5)
Hypothesis tests for one population (Chapter 6)
Comparing two populations (Chapter 7)
For the project, you need to collect you
7.2 Comparing the Means of Two Related Populations
Example 1 There are two supermarkets in a county. A resident wants determine which supermarket is
cheaper in the food products. She collected a sample from each supermarket and the prices ar
7.1 Exercise 1 A person wants to compare the heights (in meters) of a certain
type of trees in two county A and county B. He selected one sample from each
county and the results are as follows:
Sample Size n
Sample Mean x
7.1 Comparing the Means of Two Independent Populations
7.1.1 Separate-Variance t-Test (assume that the variances are not equal)
Suppose that we have two independent populations which are normally distributed. Two random
samples are selected from the two p
6.4 Hypothesis Test for Population Proportion
A sample proportion is defined as:
Part of sample
The z-statistic for a population proportion is:
p is the assumed population proportion in the null hypothesis.
7.3 Comparing Two Population Proportions
: Proportion of items of interest in population 1.
: Proportion of items of interest in sample 1.
: Proportion of items of interest in population 2.
: Proportion of items of in
6.6 Level of Significance and Type I Error
Sample Size and Type II Error
Level of Significance
We have used the level of significance in every hypothesis tests. Here we want to use some examples
to explain the meaning of the level of significance.
5.2 Confidence Interval for Population Mean ( Known)
In some situations, the population standard deviation is known. Then we can use to
construct confidence intervals which are better (more accurate) than confidence intervals constructed
using the method
6.6 Exercise 1 The following are p-values of a hypothesis test:
(a) Which of the items are significant?
(b) Which item is the most significant?
6.6 Exercise 1 Solution
6.1 Elements of Hypothesis Tests
In Chapter 5, we construct a confidence interval to estimate a population mean (or proportion). However
in many situations, we want to determine whether a population mean (or proportion) is less than,
greater than, or diff
6.5 Exercise 1 A major car manufacturer wants to test a new engine to determine
whether it meets new air pollution standards. The mean emission level must be less than
20 parts per million of carbon. Ten engines are randomly selected and the emission leve
5.1 Confidence Interval for Population Mean
For a t-distribution, the 95% confidence level corresponds the middle 95% area as follows:
The total area is 100% or 1. Then the sum of the two tail area is:
=100 95 =10.95=0.05
Each tail a
5.1 Exercise 1 A person wants to know how many times people visited a
nearby Walmart store last month in his neighborhood. A sample of four
people is surveyed and the result is as follows:
(a) What is the population? What is the sample?
6.4 Exercise 1 Last year, an insurance company paid 85.1% of the claims.
Suppose that the insurance company developed a new payment system in an
effort to increase this percentage this year. A sample of 190 claims processed
under this system revealed that
5.4 Exercise 1 The following is an Excel output:
6.2 Hypothesis Test for Population Mean
6.2.1 Left-Tailed Tests
The t-statistic is defined as
s / n
Critical Value Approach
If the t-statistic is in the rejection region, then we reject the null hypothesis
the nonrejection region, the
6.2 Exercise 1 Last month the average price of a certain type of laptops in retail
stores of a city is $465. A person wants to know whether the average price is
decreased this month. He finds the following prices in four different stores:
450 400 460 410
5.3 Confidence Interval for Population Proportion
Suppose a survey wants to determine the percentage (proportion) of people who will vote a candidate.
The survey selects a sample of 1000 people and 520 of them say that they will vote the candidate. Then
1.1 Process of statistical analysis
Identify subject of
study (the population)
Select sample (part
of the population)
present data (using
tables, graphs, etc.)
6.3 Exercise 1 Suppose the mean time from the date of service to the date of
payment for a insurance company was 41.6 days last year. The population
standard deviation = 9.9 days. A manage wants to know whether the mean time
has decreased. A sample of 4
1.2 Sample Mean and Sample Standard Deviation
Example 1 The gas prices of the gas stations on a street are as follows:
Find the sample mean and sample standard deviation.
(1) Using formulas