Hypothesis testing
Use of hypothesis testing can be very useful during decision-making connected with statistical data. A hypothesis is a statement made about a population parameter e.g. a mean and variance of a population. Hypothesis testing is a statistical process, which gives ideas or theories and then determine whether these ideas are true or false. The conclusions in hypothesis testing never 100%, therefore all tested ideas can be only probably true or probably false.

One of the most important concepts in hypothesis testing is sampling distribution. Sampling distribution is a probability distribution of sample statistics based on all possible random samples. We have to choose randomly some amount of samples to conduct testing. The more samples size we take the better our sample curve looks normally distributed. Difference between the sample mean and population mean is a sampling error. The less this error the better result of testing. Usually we take 30 samples, which are enough to draw normally distributed curve.

Typical use scenario below will make clear the real life situation when we may use Hypothesis testing: A bottled water manufacturer states on the product label that each of bottle contains 500 ml of water. We work for the government agency that protects consumers by testing product volumes. We may agree that 500 ml on the bottle is assumed to be true or we may claim it is not true. Carrying hypothesis testing we determine our null and alternative hypothesis. The hull hypothesis is what we expect to happen before we start testing. Usually, it is a statement, that is tested and denoted with “H0”. In hypothesis testing, the null hypothesis considered as true, until we have enough proof to either reject the null hypothesis, or fail to reject the null hypothesis. The alternative hypothesis usually what we do not expect to happen during testing. It is a statement, that derives when the null hypothesis reject. The alternative hypothesis are...

...Precipitation Hypothesis Testing Paper
Learning Team One
Research and Evaluation II – RES 342
University of Phoenix
Precipitation Hypothesis Testing
Learning team one will test if there is more precipitation in the three months of the spring in 2006 or is it greater than or equal to the three months in the winter in Rockville, which is located in Montgomery County, Maryland. We will look at the validity of the local average precipitation (rainfall) during the months of December through March and March through June by using the five (5) Step Hypothesis testing technique.
The testing will begin with our null and alternate hypothesis statements. Second, we will determine the level of significance or probability of rejecting the null hypothesis when it is true (Lind, Marchal, Wathwn, 2004). Third, we will select a test statistic or value from the sample. Fourth, we will formulate the decision rule, which will determine whether we accept or reject the null hypothesis. Finally, we will compare our test statistic to our critical value and decide to accept or reject the hypothesis. Our sample data will consist of spring months March 21 through June 20 and winter months December 21 through March 20.
Our learning team compared the average precipitation for the winter months of 2006 and the spring of 2006 to determine what the average precipitation between the winter...

...the representatives from MSF. What would you do if you are representing AFP? But, if you are representing MSF, how would you present your argument? (Hint: Consider your argument based on significance levels.)
8. (8 points) But, wait. What if MSF actually does not know the population standard deviation in this case, would you conduct your hypothesis test differently? Just in case that you are going to perform the hypothesis differently, what would you do instead?
The following information is for Questions 9 and 10.
The tête-à-tête between MSF and AFP broke down, as anyone would have anticipated. They are going to court.
The presiding judge, His Honor Ig Sushi, is rather apprehensive of errors in any statistical testing. Let us assume he picks a 95% significance level, an industrial standard, to be the benchmark of this court case.
I know, I know, everything sounds rather fishy......
9. (14 points) What if the RDA of cobalamine is actually not well established in the medical community? In fact, it may span a range of values in µg, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6. What is the corresponding Type II error and power for each of the given assumed RDA value?
10. (4 points) Plot the corresponding powers against the range of assumed RDA values? What do you observed in this plot, the so-called power plot? Please explain....

...Lesson note #
Statistical Inference
Testing of Hypothesis
Type I Error:
Rejection of the null hypothesis when it is true is called a type I error.
Type II Error:
Acceptance of the null hypothesis when it is false is called a type II error.
|Decision of the test for the Null Hypothesis |The Null Hypothesis is |
| |True |False |
|Accept |Correct decision |Incorrect decision |
| | |Type II Error |
|Reject |Incorrect decision |Correct decision |
| |.Type I Error | |
Test Concerning Mean
One and Two tailed Tests:
A test procedure is called a one tailed test procedure if the alternative hypothesis is one sided. The test will be two tailed if the alternative hypothesis is two sided.
Example:
Let a specified value of population mean is 45. Construct the null and alternative hypothesis for the following questions;
a) Do the sample data provide sufficient evidence to indicate that the population mean is greater than 45.
[pic] leads to one tailed...

...Hypothesis Testing Paper
Previously a group of friends compared the average temperature for the 15 days in each of the 2004 and 2005 Christmas holiday pubic school vacations to determine which holiday was colder. Secondary research retrieved from the National Oceanic and Atmospheric Administration's (NOAA) National Weather Service website provided climatic data on a daily basis for each day of the periods under investigation. Daily average temperature for each of the 15-day holiday vacation periods were gathered as two samples. The friends established a null hypothesis that the Christmas holiday vacation period of 2004 was colder than that of the 2005 Christmas holiday vacation period. After the completion of a five-step hypothesis test using a t-test, the null hypothesis was accepted. The acceptance of this null hypothesis led to further discussion on the comparison of the two periods.
The suggestion arose that perhaps the 2004 holiday vacation was colder in part due a higher occurrence of weather changes. The friends agreed that the arrival of colder winter weather always seemed to follow a period of increased winds. A new hypothesis that the colder 2004 Christmas vacation period was windier than that of 2005 was developed. The friends researched the wind speed of the holiday periods and implemented the five-step process for hypothesis testing.
Hypothesis
The average wind for the 15 days in 2004 Christmas holiday vacation is not...

...Introduction
In order to test the adverse reactions of the drug called Xynamine (a new drug designed to lower pulse rates) must be tested for their effectiveness and the drug is tested only for males. Here, the treatment groups are divided into 3 categories they were placebo group (no treatment), 10-mg treatment group and 20-mg treatment group. Thus, the analysis test result is carried out using the technique of one-way analysis of variance ANOVA (Analysis of Variance - single factor).
Assumptions of ANOVA
The assumptions of ANOVA are: Observations were randomly and independently chosen from the populations, population distributions are normal for each group; and population variances are equal for all groups.
The assumptions of ANOVA are identical to the t-test and the calculated statistic is called an F-value which has a probability value associated with it. As with the t-test, if our probability value is less than 0.05 we reject our null hypothesis (in this case that there is no difference among the treatment groups). This p-value only tells if there are significant differences among our groups. It does not tell us where these differences are. In other words, in an experiment with three treatment groups and a significant p value, we know that there are some differences among these groups but we do not know specifically which groups are different. As a result, ANOVA is usually performed in conjunction with a post hoc multiple comparisons test...

...One Sample Hypothesis Testing
The significance of earnings is a growing façade in today’s economy. Daily operation, individuals, and families alike rely heavily on each sale or paycheck to provide financial stability throughout. Depending on the nature of labor, wages are typically compensated in accords to one’s experience and education or specialization. Moreover, calculating the specified industry, occupation title, education, experience on-the-job, gender, race, age, and membership to a union will additionally influence wages. To help analyze operation pay scales and remain within budget a business should obtain data pertaining to current variations in wage. Today statistics allow a business or businesses to do so in a timely and proficient manner.
The purpose of the succeeding report is to communicate a hypothesis statement regarding the wages of Hispanics and Caucasian workers. Team B would like to determine whether race has an influence on the wage of these specific workers. Team B will convey this data of wages in both a numerical and verbal manner. Moreover, it is to describe and perform the five-step hypothesis test on the wages and wage earner data set, including data tables and results of the computations of a z-test or t-test by way of graphical and tabular methods. Also the paper will depict the results of all testing and convey how the results given Team B’s hypothesis testing may be used to answer the...

...Hypothesis Testing 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 general,
The null hypothesis (H0)...

...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 participate in the program
and each child is given a...