School

Ryerson University
Department

Quantitative Methods

Course Code

QMS 202

Professor

Jason Chin- Tiong Chan

Business Statistics II Chapter10

Chapter10 Fundamentals of Hypothesis Testing:

One-Sample tests

Outcomes:

1. Define a hypothesis and hypothesis testing

2. Describe the hypothesis-testing procedure

3. Distinguish between a one-tailed and a two-tailed test of

hypothesis

4. Conduct a hypothesis test for a population mean with known

population standard deviation

5. Conduct a hypothesis test for a population mean with unknown

population standard deviation

6. Conduct a hypothesis test for a population proportion

7. Define Type I and Type II errors

8. Compute and interpret a p-value

What is a Hypothesis?

1. A hypothesis is a statement about a population.

2. In statistical analysis we make a claim, that is, state a hypothesis, collect data,

and then use the data to test the claim.

3. In most cases the population is so large that it is not feasible to study all the

items, objects or persons in the population. For example, it would not be possible

to contact every accountant in Canada to find out his or her annual income.

4. An alternative to measuring or interviewing the entire population is to take a

sample from the population and test a statement to determine whether the

sample does or does not support the statement concerning the population.

What is Hypothesis Testing?

1. A procedure based on sample evidence and probability theory which

determine whether the hypothesis is a reasonable statement.

2. The procedure for testing a hypothesis

Step1. Define the parameter(s) of interest

Step2. State null and alternative hypotheses

Step3. Identify a level of significance

Winter2011 page#1

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Business Statistics II Chapter10

Step4. Identify the test statistic

Step5. Compute the value of test statistic and p-value

Step6. State the statistical decision and business conclusion

Note:

1. Null Hypothesis

o

H

: A statement about the value of a population parameter

Alternative Hypothesis

A

H

: A statement that is accepted if the sample

data

provide evidence that the null hypothesis is false

2. Level of significance: The probability of rejecting the null hypothesis when it

is true

3. Test Statistics: A value, determined from sample information, used to

determine whether or not to reject the null hypothesis

4. p-value : the probability of observing a sample value is as extreme as, or

more extreme than, the value observed, when the null hypothesis is

true

5. Type I error: Rejecting the null hypothesis when it is true

6. Type II error: Do not reject the null hypothesis when it is false

Winter2011 page#2

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Business Statistics II Chapter10

Example1

The BigMacBurger restaurant chain claims that the waiting time of all customers

for service is normally distributed, with a population mean of waiting time of 4

minutes and a population standard deviation of 1.4 minutes. The quality

assurance department found in a sample of 60 customers at Yonge and Dundas

that the mean waiting time was 4.1 minutes. Can we conclude that the mean

waiting time is more than 4 minutes? Test at 5% of level of significance.

Calculator Output

1-Sample z Test

µ

> 4

z

= 0.55328

p

= 0.29003

x

= 4.1

n

= 60

Step1

Let

µ

be the population mean of waiting time

Step2

4:

≤

µ

o

H

4:

>

µ

A

H

Step3

Level of significance = 0.05

Step 4

one-sample mean z test

Step5

stat

z

= 0.55328 p-value = 0.29003

Winter2011 page#3

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