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URDANETA CITY UNIVERSITY
GRADUATE SCHOOL
ADVANCED FUNDAMENTALS OF STATISTICS
THE NATURE OF STATISTICAL HYPOTHESIS
STATISTICAL INFERENCE

The theory of statistical inference consists of those methods by which one makes inferences or
generalizations about a population
2 major areas
a. estimation
 Knowledge of the sampling distribution of a proportion enables one to establish the
degree of accuracy of our estimate
b. tests of hypotheses
 you do not attempt to estimate a parameter instead, you try to arrive at a correct
decision about a pre-stated hypothesis
STATISTICAL HYPOTHESIS

it is an assertion or a statement about a population of interest

the truth or falsity of a statistical hypothesis is never known with absolute certainty unless we
examine the entire population

in practice, it is assumed that the population is so large that it is not feasible to consider all its
elements to verify the hypothesis

we use samples to check the reasonableness of the statement

evidence from the samples that is consistent with the stated hypothesis leads to its
acceptance, whereas evidence not supporting the hypothesis leads to its rejection
STATISTICAL HYPOTHESIS TESTING

it is a procedure of dichotomizing the conflicting theories and test these statements based
from the sample evidence and probability theory

at the end of this procedure, you can “reject” or “do not reject” the assumed true hypothesis

the acceptance of a hypothesis merely implies that the data do not give sufficient evidence to
refute it.

Rejection implies that the sample evidence refutes it

Put another way, rejection means that there is a small probability of obtaining the sample
information observed when, in fact, the hypothesis is true.
The logic of hypothesis testing can be stated in three steps:
1 A hypothesis concerning a population is stated.
2 A sample is selected from the population.
3 The sample data are used to determine whether the hypothesis can reasonably be
supported or not. Ultimately, the conclusion drawn is about the population not just
the sample.



Information about a population will be presented in one of two forms, as a mean (µ) or as a
proportion (p)

Use the population mean (µ) in the hypothesis statements when the question gives you
information about the population in the form of an average
 e.g. “the average travel time was 40 minutes…”, µ = 40 minutes

Use the population proportion (p) in the hypothesis statements when the question gives you
information about the population in the form of a fraction, percentage, or decimal
 e.g. “ 4 out of 5 dentists agree…”, p = ⅘ or p = 80% or p = .80
THE NULL HYPOTHESIS and THE ALTERNATIVE HYPOTHESIS
NULL HYPOTHESIS

Denoted by Ho

Always assumed to be true before performing the test

Sometimes, it is referred as the status quo

In practice, it is expressed as a statement concerning the value of a population parameter (say
the mean)

The Null Hypothesis is the stated or assumed value of a population parameter (the
mean or proportion that is being analyzed)
 What the question says the population is doing
 The current or reported condition

The necessary information tends to be in the first sentence of the problem

When trying to identify the population parameter needed for your solution, look for the
following phrases:



 “It is known that…”
 “Previous research shows…”
 “The company claims that…”
 “A survey showed that…”
When writing the Null Hypothesis, make sure it includes an “=” symbol. It may look
like one of the following:
 e.g. H0: µ = 40 minutes
 e.g. H0: µ ≤ 40 minutes
 e.g. H0: µ ≥ 40 minutes

ALTERNATIVE HYPOTHESIS

Denoted by H1 or Ha

Describes the consequence of rejecting the null hypothesis

Often called the research hypothesis since it is the alternative that the researchers want to get

The Alternate Hypothesis is the stated or assumed value of a population parameter if the
Null Hypothesis (H0) is rejected (through testing)

The necessary information tends to be found in the last sentence of the problem (or the
sentence ending in a “?”)

When trying to identify the information needed for your Alternate Hypothesis
statement, look for the following phrases:
 “Is it reasonable to conclude…”
 “Is there enough evidence to substantiate…”
 “Does the evidence suggest…”
 “Has there been a significant…”

There are three possible symbols to use in the Alternate Hypotheses, depending on the
wording of the question

Use “≠” when the question uses words/phrases such as:
 “is there a difference...?”
 “is there a change...?”

Use “<” when the question uses words/phrases such as:
 “is there a decrease…?”
 “is there less…?”
 “are there fewer…?”

Use “>” when the question uses words/phrases such as:
 “is there a increase…?”
 “is there more…?”

When writing the Alternate Hypothesis, make sure it never includes an “=” symbol. It
should look similar to one of the following:
 e.g. H1: µ < 40 minutes
 e.g. H1: µ > 40 minutes
 e.g. H1: µ ≠ 40 minutes
Exercises
A recent survey of college campuses across Ontario claims that students spend an average of
2.7 hours a day using their cell phones. A random sample of 35 Durham College students
showed an average use of 2.9 hours a day, with a standard deviation of 0.4 hours. Do Durham
College students use their cell phones more than the typical Ontario college student?

A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3
times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2
weeks.
A researcher is studying the effects of radical exercise program on knee surgery patients. There is a
good chance the therapy will improve recovery time, but there’s also the possibility it will make it
worse. Average recovery times for knee surgery patients is 8.2 weeks.
Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic.
The heart will last and operate almost indefinitely once it is implanted in the patient’s body, but the
battery pack needs to be recharged about every four hours. Is there evidence to support the claim
that the mean battery life exceeds 4 hours?
A random samples of 100 deaths in the Philippines last year showed an average life span of 69.3
years. Assuming a population standard deviation of 7.8 years, does this seem to indicate that the life
span today is lesser than 70 years?

Prepared by:
christian paul e. gonzales, rn,
shilanlee dagdag, rn

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