Step 1: Formulate the null and alternative hypothesis. Draw the one-tail or two- tail test diagram.

Step 2: Specify the level of significance. Determine the critical value (s).

Step 3: Identify the test statistics to be used and calculate it.

Step 4: Draw the conclusion.

Formulae List
Hypothesis Testing

Test Statistics for Single Mean| | Test Statistics for Two Means| known| | 1 and 2 known|
z* = x-μ0σn| | z* = x1-x2-δ0σ12n1+σ22n2|
unknown and n > 30| | 1, 2 unknown and n1 n2 2 30|
z* = x-μ0sn| | z* = x1-x2-δ0s12n1+s22n2|
unknown and n < 30| | 1, 2 unknown and n1 n2 2 < 30|
t* = x-μ0σn df = n 1| | t* = x1-x2-δ0s12n1+s22n2 df = n1 + n2 2|

Test Statistics for Single Proportion| | Test Statistics for Two Proportions| z* = Ps-P0P01-P0n| | z* = Ps1-Ps2-δ0Ps11-Ps1n1+Ps21-Ps2n2|

Using Excel

Z-score: Use =NORM.S.INV() function.

t-statistics: Use =TINV() function.
-------------------------------------------------

Use the above steps and formulae; solve the following questions using Excel and write down the solution on MS Word.

Question 1

The Safe Appliance Store issues its own credit card. The credit manager wants to find whether the mean monthly unpaid balance is more than $400. The level of significance is set at 0.05. A random check of 172 unpaid balances revealed the sample mean is $407 and the standard deviation of the sample is $38.

Should the credit manager conclude that the population mean is greater than $400?

Question 2

A machine is set to fill a specially designed bottle with 9.0 grams of vitamins. It is claimed that the mean is less than 9.0 grams. The hypothesis is to be tested at the 0.01 level.

...APP6JMaloney problems 2. 4, 6, 10, 18, 22, 24
2 ) The value of the z score un a hypothesis test is influenced by a variety of factors.
Assuming that all the other variables are held constant, explain how the value
of Z is influenced by each of the following?
Z= M - u / SD
a) Increasing the difference between the sample mean and the original.
The z score represents the distance of each X or score from the mean.
If the distance between the sample mean and the population mean the z score will
increase.
b) Increasing the population standard deviation.
The standard deviation is the factor that is used to divide by in the equation. the bigger the SD,
then the smaller the z score.
c) Increasing the number of scores in the sample.
Should bring the samples mean closer to the population mean so z score will get smaller.
4) If the alpha level is changed from .05 to .01
a) what happens to the boundaries for the critical region?
It reduces the power of the test to prove the hypothesis.
You increase the chance of rejecting a true H
b) what happens to the probability of a type 1 error?
Type 1 error is falsely reporting a hypothesis,
Where you increase the chance that you will reject a true null hypothesis.
6) A researcher is investigating the effectiveness of a new study skills training program for elementary
school childreen. A sample of n=25 third grade children is selected to...

...all, the video did a fair job buttressing my understanding of hypothesistesting. The textbook explained the aspects and steps of hypothesistesting in a legible fashion, while the video helped demonstrate a real-life application.
I learned from the text that hypothesistesting is a “Procedure for deciding whether the outcome of a study (results from a sample) supports a particular theory or practical innovation (which is thought to apply to a population)” (Aron A., Aron, E., and Coups, 2011, p. 145). I also learned that hypothesistesting follows a set procedure that appears as follows:
Step 1) Restate the question as a research hypothesis and a null hypothesis about the populations
- Basically, a researcher constructs a hypothesis. Then he/she forms a null hypothesis that opposes the research hypothesis in
polar fashion. To help support one’s research hypothesis, one has to disprove the null hypothesis.
Step 2) Determine the characteristics of the comparison distribution
- When using two or more samples, one must gather information about the distribution of means.
Step 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be...

...HypothesisTesting I
Pat Obi
What is a “Hypothesis?”
A statement or claim about the value of a
population parameter: μ, σ2, p
Pat Obi, Purdue University Calumet
2
Decision Rule
1.
x 0
Z
s
n
Compare calculated Z value to Z value from
Table (critical Z value)
Reject H0 if calculated Z value lies in the
rejection/significance region (i.e. region)
ALTERNATIVELY:
2.
Compare p-value to
Reject H0 if p-value <
Pat Obi, Purdue University Calumet
3
Two-Tail Test
Ex: H0: 0 = 50; H1: 0 ≠ 50. Test at α = 0.05
Reject H0 if calculated Z is either less than ZCV
on the left tail or greater than ZCV on the right
0
Rejection region: /2 = 0.025
Rejection region: /2 = 0.025
0
ZCV = -1.96
ZCV = 1.96
Pat Obi, Purdue University Calumet
4
One-Tail Test: Right/Upper Tail
Ex: H0: 0 ≤ 55; H1: 0 > 55. Test at α = 0.05
Reject H0 if calculated Z > Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = 1.645
Pat Obi, Purdue University Calumet
5
One-Tail Test: Left/Lower Tail
Ex: H0: 0 ≥ 12; H1: 0 < 12. Test at α = 0.05
Reject H0 if calculated Z < Table Z (i.e. Zcv)
0
Rejection region: = 0.05
ZCV = -1.645
Pat Obi, Purdue University Calumet
6
Z Table (critical Z values)
Significance
Level
Zcv
One-Tail Test
Zcv
Two-Tail Test
0.10
1.285
1.645
0.05
1.645
1.960
0.01
2.326
2.576
Pat Obi, Purdue University Calumet
7
Rules Governing the Statement of
Hypothesis
In...

...HYPOTHESISTESTING
WHAT IS THIS HYPOTHESIS????
• In simple words it means a mere assumption or supposition to be proved of disproved.
• But, for a researcher it is a formal question that he intends to resolve.
• Example: I assume that 1) under stress and anxiety a person goes into depression.
2) It leads to aggressive behaviour.
Eg. : Students who get better counselling in a university will show a greater increase in creativity than students who were not counselled.
• So, the hypothesis should be capable of being verified and tested.
CHARACTERISTICS
• Should be clear and precise – inferences not reliable
• Capable of being tested
“ A hypothesis is testable if other deductions can be made from it which, in turn can be confirmed or disproved by observation.”
• Should be limited in scope and must be specific
• Should be stated in simple terms -understandable by all concerned.
• Must explain the facts that gave rise to the need for explanation.
BASIC CONCEPTS: NULL & ALTERNATIVE HYPOTHESIS
• If we are to compare two methods A & B and both are equally good, then this assumption is termed as null hypothesis(H0)
• If it is stated that method A is better than method B-alternative hypothesis(Ha)
LEVEL OF SIGNIFICANCE
• A very important concept in the context of hypothesistesting
• It is represented in a % age...

...CHAPTER
8
Introduction to
HypothesisTesting
8.1
Inferential Statistics
and HypothesisTesting
LEARNING OBJECTIVES
8.2 Four Steps to
HypothesisTesting
After reading this chapter, you should be able to:
8.3
HypothesisTesting and
Sampling Distributions
8.4
Making a Decision:
Types of Error
8.5
Testing a ResearchHypothesis: Examples
Using the z Test
8.6
Research in Focus:
Directional Versus
Nondirectional Tests
8.7
Measuring the Size of
an Effect: Cohen’s d
8.8
Effect Size, Power, and
Sample Size
8.9
Additional Factors That
Increase Power
1 Identify the four steps of hypothesistesting.
2 Define null hypothesis, alternative hypothesis,
level of significance, test statistic, p value, and
statistical significance.
3 Define Type I error and Type II error, and identify the
type of error that researchers control.
4 Calculate the one-independent sample z test and
interpret the results.
5 Distinguish between a one-tailed and two-tailed test,
and explain why a Type III error is possible only with
one-tailed tests.
6 Explain what effect size measures and compute a
Cohen’s d for the one-independent sample z test.
7 Define power and identify six factors that influence power....

...27 April 2014
Submission date: 9 May 2014
TUTORIAL ON HYPOTHESISTESTING (1)
Basic Concept
1. State the null and alternative hypothesis for each conjecture :
a. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 3.0kg.
b. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 8.
c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean score was 73.
d. The average time to read a certain passage is 15 minutes. An educator claimed that a course in speed reading will shorten the reading time.
e. A chemist said that he invested an additive which can increase the life of batter. The mean lifetime is 24 months.
f. The mean waiting bus for buses in Klang Valley is 8 minutes. Some roads are restricted to buses only during office hours. A test is performed to see how this has affected the mean waiting time.
2. Determine whether the one-tailed test or two-tailed test is appropriate for the situation given below:
a. Testing whether the newly-purposed highway speed limit increases the number of accidents.
b....

...Nonparametric HypothesisTesting Paper
ABC’s real estate agency has recently expanded its business and is in the process of conducting research on housing prices within 10 miles of its new office. Team B has been given the task by ABC real estate to conduct the needed research. The team will be able to answer at the end of the research if the prices in Santa Cruz, California, are less than the prices of house in Scott’s Valley, California. Throughout this research process the team will formulate the hypothesis statement, perform a five-step hypothesis test, discuss which nonparametric test was needed, and discuss the results from this data research compare to past research completed.
Five-Step Hypothesis Test
The five-step hypothesis test will determine if consumers have a greater satisfaction when the consumer(s) pay more for the home.
Step one is to state the null hypothesis and alternative hypothesis:
Ho: µ1 = µ2 No difference in satisfaction
Ho: µ1≠ µ2 Satisfaction differs for the two groups
Step two evaluates if the assumptions have been met through the Mann-Whitney test selection that will compare the two populations and will assume equal variances with a 95% confidence level, the significance level is .05. The decision rule is to reject Ho if z>1.645.
Step three the ranks are summed and calculated using the Wilcoxon – Mann-Whitney test....

...HypothesisTesting For a Population Mean
The Idea of HypothesisTesting
Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test:
H0: = 190
H1: > 190
We test 100 only children and find that
x = 198
and suppose we know the population standard deviation
= 15.
Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have
z is called the test statistic.
Since z is so high, the probability that Ho is true is so small that we decide to reject H0 and accept H1. Therefore, we can conclude that only children have a higher average cholesterol level than the national average.
Rejection Regions
Suppose that = .05. We can draw the appropriate picture and find the z score for -.025 and .025. We call the outside regions the rejection regions.
We call the blue areas the rejection region since if the value of z falls in these regions, we can say that the null hypothesis is very unlikely so we can reject the null hypothesis
Example
50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less...

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