Okay, let me try to analyze this step-by-step: 1) Null Hypothesis (H0): The advertisement had no effect on sales. 2) Alternative Hypothesis (H1): The advertisement increased sales. 3) We can test this using a paired t-test, since we have sales data from the same shops before and after. 4) Calculate the mean difference between before and after sales for each shop. Then take the average of those differences. 5) Use the t-statistic to determine if the average difference is significantly greater than 0, which would indicate the advertisement increased sales. So in summary, a paired t-test can be used to determine if the advertisement

1. Mean Test

2. Chapter 9,
Hypothesis Testing
 Developing Null and Alternative Hypotheses
 Type I and Type II Errors
 Population Mean: s Known
 Population Mean: s Unknown
 Population Proportion

3. Introduction
Assumption about population parameter is
hypothesis. Process of testing its validity is known as
hypothesis testing. i.e. claim about something is
hypothesis and process of testing its validity is
hypothesis testing.

4. Null and alternative hypothesis
Null hypothesis: Assumption about population
parameter is null hypothesis. Here we assume that
there is not significant difference between assumed
value and true value. It is denoted by Ho. The null
hypothesis is written in terms of population. For eg. If
we wish to test average marks of Student in statistics in
MBA I term is 75 or not then null hypothesis is
Ho:μ=75

5. Alternative hypothesis
One inference may the null hypothesis is considered
false ,something else must be true.
Whenever a null hypothesis is specified, an alternative
hypothesis is also specified, and it must be true when
null hypothesis is false. In other words any hypothesis
that is true when null hypothesis is false is called
alternative hypothesis.
Alternative hypothesis is denoted by H1

6. Continue
I f we wish that Class of Statistics was properly
handled by Mr Nirajan Bam So average marks of
Student is 75 .This is stated as
Ho:μ =75 Vs H1:μǂ 75 (Two tailed test)
Again if we assume that Class of Statistics was properly
handled by Mr Nirajan Bam So average marks of
Student is more than 75 .This is stated as

7. Continue
Ho:μ=75 Vs H1:μ>75 (Right tailed test)
Again if Dean of PU assume that
Class of Statistics was not properly handled by Mr
Nirajan Bam So average marks of Student is Less than
55 .This is stated as
Ho:μ=55 Vs H1:μ<55 (Left tail test)

8. Some key points regarding Null and
alternative hypothesis
Ho represents current belief in a situation
H1 is opposite of null hypothesis and represents a
research claim or specific claim you would like to
prove.
Ho always refers to specified value of the population
parameter.
In alternative hypothesis we placed not equal sign or <
sign or > sign on the basis of our claim

9. Developing Null and Alternative Hypotheses
• It is not always obvious how the null and alternative
hypotheses should be formulated.
• Care must be taken to structure the hypotheses
appropriately so that the test conclusion provides
the information the researcher wants.
• The context of the situation is very important in
determining how the hypotheses should be stated.
• In some cases it is easier to identify the alternative
hypothesis first. In other cases the null is easier.
• Correct hypothesis formulation will take practice.

10. Developing Null and Alternative
Hypotheses
Alternative Hypothesis as a Research Hypothesis
• Many applications of hypothesis testing involve
an attempt to gather evidence in support of a
research hypothesis.
• In such cases, it is often best to begin with the
alternative hypothesis and make the conclusion
that the researcher hopes to support.
• The conclusion that the research hypothesis is true
is made if the sample data provide sufficient
evidence to show that the null hypothesis can be
rejected.

11. Developing Null and Alternative
Hypotheses
 Alternative Hypothesis as a Research Hypothesis
• Example:
A new teaching method is developed that is
believed to be better than the current method.
• Alternative Hypothesis:
The new teaching method is better.
• Null Hypothesis:
The new method is no better than the old method.

12. Developing Null and Alternative Hypotheses
 Alternative Hypothesis as a Research Hypothesis
• Example:
A new sales force bonus plan is developed in an
attempt to increase sales.
• Alternative Hypothesis:
The new bonus plan increase sales.
• Null Hypothesis:
The new bonus plan does not increase sales.

13. Developing Null and Alternative Hypotheses
 Alternative Hypothesis as a Research Hypothesis
• Example:
A new drug is developed with the goal of lowering
blood pressure more than the existing drug.
• Alternative Hypothesis:
The new drug lowers blood pressure more than
the existing drug.
• Null Hypothesis:
The new drug does not lower blood pressure more
than the existing drug.

14. Developing Null and Alternative
Hypotheses
Null Hypothesis as an Assumption to be Challenged
• We might begin with a belief or assumption that
a statement about the value of a population
parameter is true.
• We then using a hypothesis test to challenge the
assumption and determine if there is statistical
evidence to conclude that the assumption is
incorrect.
• In these situations, it is helpful to develop the null
hypothesis first.

15. Developing Null and Alternative Hypotheses
 Null Hypothesis as an Assumption to be Challenged
• Example:
The label on a soft drink bottle states that it
contains 67.6 fluid ounces.
• Null Hypothesis:
The label is correct. m = 67.6 ounces.
• Alternative Hypothesis:
The label is incorrect. m ǂ 67.6 ounces.

16. Class work
The statistics department installed energy-efficient
lights, heaters, and air conditioners last year. Now they
want to determine whether the average monthly
energy usage has decreased. Should they perform the
one tailed or two tailed test? If their previous monthly
energy usage was 3,124 kilo watt hours, what are the
null and alternative hypothesis

17. Summary of Forms for Null and Alternative
Hypotheses about a Population Mean
 The equality part of the hypotheses always appears
One-tailed
(lower-tail)
One-tailed
(upper-tail)
Two-tailed
H0 : m  m0
0 : a H m  m
0 0 H : m  m
0 : a H m  m
0 0 H : m  m
0 : a H m  m
in the null hypothesis.
 In general, a hypothesis test about the value of a
population mean m must take one of the following
three forms (where m0 is the hypothesized value of
the population mean).

18. Null and Alternative Hypotheses
Example: Metro EMS
A major west coast city provides one of the most
comprehensive emergency medical services in the
world. Operating in a multiple hospital system
with approximately 20 mobile medical units, the
service goal is to respond to medical emergencies
with a mean time of 12 minutes or less.
The director of medical services wants to
formulate a hypothesis test that could use a sample
of emergency response times to determine whether
or not the service goal of 12 minutes or less is being
achieved.

19. Type I Error
 Because hypothesis tests are based on sample data,
we must allow for the possibility of errors.
 A Type I error is rejecting H0 when it is true.
 The probability of making a Type I error when the
null hypothesis is true as an equality is called the
level of significance.
 Applications of hypothesis testing that only control
the Type I error are often called significance tests.
Type I error is also called producers risk.

20. Type II Error
 A Type II error is accepting H0 when it is false.
 It is difficult to control for the probability of making
a Type II error.
 Type II error is denoted by β and is called
Consumers risk.
(1-β) is called power of the test i.e probability of
Correct decision is called power of the test

21. Types of error in Hypothesis
Testing
Actual Situation
Statistical decision Ho is true Ho is false
Do not reject Ho
Correct
Decision=(1-α)
Type II error
P(Type II error)=β
Reject Ho Type I error
P(Type I error)=α
Correct decision
Power of test =1-β
Producers risk
Consumers Risk

22. Critical value
Critical value is a tabulated value which separates
acceptance region and rejection region.

23. Two-Tailed Tests About a Population Mean:
s Known
 Critical Value Approach
Do Not Reject H Reject H0 0
a/2 = .015
0 2.17
z
Reject H0
-2.17
Sampling
distribution
x
of z
n

m
s
0
/
a/2 = .015

24. Significance Levels and p-values
Significance Level
• A critical probability associated with a statistical hypothesis
test that indicates how likely an inference supporting a
difference between an observed value and some statistical
expectation is true.
• The acceptable level of Type I error.
p-value
• Probability value, or the observed or computed significance
level.
p-values are compared to significance levels to test hypotheses.
Higher p-values equal more support for an hypothesis.
21–24

25. Steps of Hypothesis testing
Set null and alternative hypothesis
Select a level of significance
Identify test statistics and its sampling distribution.
General idea of sampling distribution is as below

26. s Known s Unknown
Sample size size
greater than 30
Z-test Z-test
Sample size is less
than or equal to 30
Z-test T-test

27. Steps of Hypothesis testing
continue
Define test statistic and compute it
Obtain the critical value
Conclusion: If Calculated value is less than tabulated
value then Ho is accepted otherwise Ho is rejected

28. Examples
For a sample of 60 women taken from a population of
over 5,000 enrolled in a weight-reducing program at a
nationwide chain of health spas, the sample mean
diastolic blood pressure is 101 and sample standard
deviation is 42.At a significance level of 0.02, on
average, did the women enrolled in the program have
diastolic blood pressure that exceeds the value of 75

29. Example 2
Realtor Elaine Snynderman took a random sample of
12 homes in a prestigious suburb of Chicago and found
the average appraised market value to be 780,000, and
the standard deviation was 49,000.Test the hypothesis
that for all homes in the area, the mean appraised
value is $ 825,000 against the alternative that it is less
than $825,000.Use 0.05 level of significance

30. Example 3
A television documentary on overeating claimed that
Americans are about 10 pounds overweight on average.
To test this claim , eighteen randomly selected
individuals were examined; Their average excess
weight was found to be 12.4 pounds, and Sample SD
2.7 pounds. At a significance level 0.01 ,Is there any
reason to doubt the validity of the claimed 10-pounds
value

31. Classwork
The policy of a particular bank branch is that its ATMs
must be stocked with enough cash to satisfy customers
making withdrawals over an entire weekend. Customer
goodwill depends on such services meeting customer
needs. At this branch the expected (i.e. population) mean
amount of money withdrawn from ATMs per customer
transaction over the weekend is $ 160 with an expected (i.e.
population) standard deviation of $30. Suppose that a
random sample of 36 customer transaction is examined
and it is observed that the sample mean withdrawal is $ 172.
At the 0.05 level of significance, is there evidence to believe
that the true mean withdrawal is greater than $ 160?

32. Classwork
The policy of a particular bank branch is that its ATMs
must be stocked with enough cash to satisfy customers
making withdrawals over an entire weekend. Customer
goodwill depends on such services meeting customer
needs. At this branch the expected (i.e. population) mean
amount of money withdrawn from ATMs per customer
transaction over the weekend is $ 1500 with an expected
(i.e. population) standard deviation of $300. Suppose that a
random sample of 64 customer transaction is examined
and it is observed that the sample mean withdrawal is $
1720. At the 0.05 level of significance, using the p-value
approach to hypothesis testing, is there evidence to believe
that the true mean withdrawal is greater than $ 1500?

33. Example 4
A sample of 32 money-market mutual funds was
chosen on January 1 1996.And the average annual rate
of return over the past 30 days was found to be 3.23 %
and the sample standard deviation 0.51 percent. A year
earlier, a sample of 38 money-market funds showed an
average rate of return of 4.36% with Sd 0.84% .Is it
reasonable to conclude (at 0.05) that money-market
interest rates decline during 1995

34. Example no: 5
A sample of 30 year conventional mortgage rates at 11
randomly chosen Banks in California yielded a mean
rate of 7.61 percent and standard deviation of 0.39
percent. A similar sample taken at randomly chosen
banks in Pennsylvania had mean rate of 7.43%,and
standard deviation of 0.56%.Do these samples provide
evidence to conclude (at 0.01) that conventional
mortgage rates in California and Pennsylvania Come
from population with different means?

35. Example no 6
A member of public interest groups concerned with
environment pollution asserts at public hearing that
“fewer than 60% of the industrial plants in this area
are complying with air pollution standard “. The
officials samples 60 plants and finds that 33 are
complying with air pollution standard. Is the asserting
by the member of public interest group a valid one?
Test the hypothesis at the 0.02 significance level.

36. Example no:7
In 1991 it was believed that 41% of companies had their
own ethics codes. In a 1999 survey conducted by
conference board, 97 of 124 companies indicated that
they have their own ethics codes. At the 0.01 level of
significance, is there evidence that the proportion has
increased from the previous value of 0.41?

37. Example no:8
Two different large groups of people are being
considered as focus group for reading English
newspaper. Of 200 people surveyed in one group (the
government employees), 52 percent read the English
newspaper. In another group (private employees), 40
percent of the 150 people surveyed read the English
newspaper. At the 0.05 level of significance, is there
evidence to conclude that there is significantly higher
percentage of government employees who read English
newspaper than do private employees?

38. Class work
Are whites more likely than blacks to claims bias? A
survey conducted by Barry Goldman, found that of 56
white workers terminated, 29 claimed bias. Of 407
black workers terminated, 126 claimed bias At the 0.05
level of significance, is there evidence that white
workers are more likely to claim likely to claim bias
than black workers?

39. Example no:9
A survey of investors who have Internet access divided these into
two groups, those who trade online and those who do not
(traditional traders). Of the traditional investors 48% were
bullish on the market, and of the online investors 69% were
bullish on the market. Suppose that the survey was based on 500
traditional investors and 500 online investors.
At the 0.05 level of significance, is there a significant difference
between the proportion of traditional and online investors who
are bullish on the market?

40. 1.The sales of an items in eight shops before
and after advertisement is given as:
Test whether advertisement was effective or
not.
Before 70 65 48 72 80 92 98 100
After 72 70 53 75 84 95 105 104