Hypothesis Testing For a Population Mean
The Idea of Hypothesis Testing
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 sleep than the general public which needs an average of 7.7 hours of sleep. We follow the steps below.

Compute a rejection region for a significance level of .05. If the sample mean is 7.5 and the population standard deviation is 0.5, what can you conclude?
Solution
First, we write write down the null and alternative hypotheses H0: = 7.7 H1: < 7.7 This is a left tailed test. The z-score that corresponds to .05 is -1.645. The critical region is the area that lies to the left of -1.645. If the z-value is less than -1.645 there we will reject the null hypothesis and accept the...

...report aims to analyse and interpret the data set of 200 records regarding the CCResort. The given information includes booking identification number, income, number of people per booking, length of stay, age and overall expenditure.
From the booking ID it can be assumed that the selection of data is random, however as it is only partial information and not the population, the period of time in which the data is selected from would affect the end results of analysis.
The report is divided into two sections outlining the statistical analysis of data and hypothesistesting to observe if CCResort have met their 2 major key performance indicators (KPIs)
1 More than 40% of their customers stay for a full week (i.e. seven nights);
2 The average customer spends more than $255 per day in excess of accommodation costs.
Figures at a glance
This section of the report aims to give users a better understanding of the data through statistical data analysis of investigation categories including family income, expenditure habits, age distribution, the number of people per booking and their length of stay. These analysis are meaningful in giving users a better understanding of the customer base in relation to the key performance indicators.
1. Family income distribution
From the data collected, 62 families (31% of the sample) earn an income of more than $100,000 while 69% of the sample (138...

...TEMASEK POLYTECHNIC
SCHOOL OF INFORMATICS & IT
Quantitative Techniques
Lab 5 (Topic 3: HypothesisTesting)
-------------------------------------------------
Procedure for HypothesisTesting
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
HypothesisTesting
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...

...HypothesisTesting: Two-Sample Case for the Mean
Many cases in the social sciences involve a hypothesis about the difference between two groups (i.e. men and women, control and experiment). We analyze statistics from two samples, and the hypothesis and confidence interval would deal with the difference between two population means. The following factors are important in hypothesistesting:
1. probability theory
2. the sampling distribution of the statistic
3. the errors inherent in hypothesistesting and estimation
4. the level of significance and the level of confidence
5. the directional nature of the alternative hypothesis
General Procedure
1. State the hypotheses.
2. Set the criterion for rejecting H0.
3. Compute the test statistic.
4. Construct the confidence interval.
5. Interpret the results.
Hypothesis of Differences
• There is no difference between mean of group 1 and the mean of group 2.
• [pic] or [pic]
o to test this difference, we determine the difference between the statistic (the difference between the means), and the hypothesized value for the parameter (0).
o if the population variance is known, the sampling distribution of differences is normally distributed.
o if the population variance is UNKNOWN, the...

...Why We Don’t “Accept” the Null Hypothesis
by Keith M. Bower, M.S. and James A. Colton, M.S.
Reprinted with permission from the American Society for Quality
When performing statisticalhypothesis tests such as a one-sample t-test or the AndersonDarling test for normality, an investigator will either reject or fail to reject the null
hypothesis, based upon sampled data. Frequently, results in Six Sigma projects contain
the verbiage “accept the null hypothesis,” which implies that the null hypothesis has been
proven true. This article discusses why such a practice is incorrect, and why this issue is
more than a matter of semantics.
Overview of HypothesisTesting
In a statisticalhypothesis test, two hypotheses are evaluated: the null (H0) and the
alternative (H1). The null hypothesis is assumed true until proven otherwise. If the
weight of evidence leads us to believe that the null hypothesis is highly unlikely (based
upon probability theory), then we have a statistical basis upon which we may reject the
null hypothesis.
A common misconception is that statisticalhypothesis tests are designed to select the
more likely of two hypotheses. Rather, a test will stay with the null hypothesis until
enough evidence (data) appears to...

...Running head: MULTIPLE SAMPLE HYPOTHESISTESTING
Multiple Sample HypothesisTesting
RES342: Research 11
June 14, 2010
Multiple Sample HypothesisTesting
The purpose of this paper is to create a hypothesis based on two-sample tests. Two-sample tests compare two sample estimates with each other, whereas one-sample tests compare a sample estimate with a non-sample benchmark (Doane & Seward, 2007). The learning team has chosen to create a hypothesistesting using the wages and wage earners data set. The learning team has developed one business research question from which the team will formulate a research hypothesis. The business research question and testing simply involves creating two separate groups of the data set, and testing whether a difference in the mean of the earnings in both the older group, ages 42-64 and the younger group, ages 18-41 exists. To create a solid testinghypothesis, the team has formulated both a numerical and verbal hypothesis statement, conducted the five-step hypothesis test on the data, and presented a description of the test results by explaining how the discoveries from the hypothesistesting can be used to answer the research question.
Learning Team A believes that there are...

...Application of statistical concepts in the determination of weight variation in samples
G.E.
Institute of Biology, College of Science
University of the Philippines, Diliman, Quezon City, Philippines
Date Submitted: April 23, 2013
ABSTRACT
Statistics is a mathematical science dealing with the collection, organization, analysis, interpretation, and presentation of data. It provides a more accurate way of expressing data rather than mere observation. This experiment used the different statistical concepts such as the Q test, mean, standard deviation, relative standard deviation, range, relative range, and confidence limits or confidence intervals. The results generated from these tests are used as a basis to check whether the values obtained from weighing 10, 25 centavo coins using an analytical balance and which were grouped into two data sets, are acceptable or not. It can be seen that when the statistical concepts were applied to data set 1 and data set 2, the resulting values obtained do not greatly vary. However, it can’t be proven that the results do not differ significantly since there was no test performed to check this.
RESULTS AND DISCUSSION
Different weights were obtained from the 10- 25 centavo coins using the analytical balance. Each weight is considered as a single sample. The samples were grouped into two data sets. The first dataset contains six samples while the second data set contains 10 samples. The...

...Nonparametric HypothesisTesting Paper
Team B
RES 342
Eric Hogan
University of Phoenix
Nonparametric HypothesisTesting
Nonparametric testing does not depend on certain data in a particular distribution. Also, nonparametric testing applies techniques that do not assume that the basis of a model is predetermined. In a previous paper we discussed a hypothesis with single and double samples. Now we will conduct the equivalent, nonparametric test of the real estate hypothesis using another five-step process. The testing we will use in this paper will be the Wilcoxon Signed-Rank Test. The Wilcoxon Signed-Rank Test compares a single sample median with a benchmark using only ranks of data instead of the original observations. It is used to compare paired observations. An advantage of the Wilcoxon Signed-Rank Test is the freedom from the normality assumption. Other advantages are robustness to outliers and applicability to ordinal data (David P. Doane, 2007). In the Wilcoxon Signed-Rank Test the population should have a lot of similarity. The data should have some correlation like houses and price for example. Our hypothesis is as stated: If a real estate home has 3 bedrooms or more, then the price is at least 200,000 dollars or more. The possible outcomes for the tests are left-tailed, two-tailed and right-tailed. The...

...Throughout life, we all make educated guess; explaining a set of observation and derive and write and formulized hypothesis (Formalized Hypotheses example: If skin cancer is related to ultraviolet light , then people with a high exposure to uv light will have a higher frequency of skin cancer). There are three types of scientific statements: there are Hypothesis, Law and Theory.
A hypothesis will give a plausible explanation that will be tested. It can also explain future phenomenon that will need to be tested. Once a hypothesis has been widely accepted, it is called a law. This means that it is assumed to be true and will predict the outcome of certain conditions or experiments. Some laws cannot yet be proven because technology to test them has not been invented.
A scientific theory is broader in scope and explains more events that a law. After hypotheses and laws have been tested many times, with accurate results, they become theories.
Hypothesis is a prediction about the outcome of a study that will hold-up or be true for the population at large. We should not confuse a hypothesis for a theory which is explanations base on a large amount of date.
The key word is testable. That is, you will perform a test of how two variables might be related. This is when you are doing a real experiment. You are testing variables. Usually, a hypothesis is based on some...