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 statistical hypothesis 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 Hypothesis Testing
In a statistical hypothesis 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 statistical hypothesis 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 support the alternative.

The amount of evidence required to “prove” the alternative may be stated in terms of a confidence level (denoted X%). The confidence level is often specified before a test is conducted as part of a sample size calculation. We view the confidence level as equaling one minus the Type I error rate (α). A Type I error is committed when the null hypothesis is incorrectly rejected. An α value of 0.05 is typically used, corresponding to 95% confidence levels.

The p-value is used to determine if enough evidence exists to reject the null hypothesis in favor of the alternative. The p-value is the probability of incorrectly rejecting the null hypothesis.
The two possible conclusions, after assessing the data, are to: 1....

...* the number possible outcomes that you are interested in divided by the total number of possible outcomes associated with an event
* nullhypothesis significance testing (NHST)
* the nullhypothesis states that there is no effect in the population of interest
* if the probability of obtaining the data is high, the nullhypothesis is true
* no effect in the...

...Hypothesis Testing
* Used to prove which are the factors that are actually impacting the mean or standard deviation of the project y.
* To see the impact of improvements after they are implemented
* P- value is critical in making decisions.
* To determine if the statistical hypothesis is true or false, the entire population should be examined, which becomes impossible for large sizes, Random sampling is done.
* The conclusion for the...

...above information, what kind of hypothesis test will you conduct? The y-test, z-test, t-test, χ2-test, F-test, G-test, or even the y-not-test? Please explain.
4. (2 points) What will be the nullhypothesis, the alternative hypothesis, and, hence, the "tailedness" of the test (left-tailed, right-tailed, or two-tailed)?
5. (10 points) What is be the corresponding test statistics?
6. (8 points) What is the...

...Running head: MULTIPLE SAMPLE HYPOTHESIS TESTING
Multiple Sample Hypothesis Testing
RES342: Research 11
June 14, 2010
Multiple Sample Hypothesis Testing
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...

...Take Home Test 2
1. A. NullHypothesis: There are no relations or associations among the groups’ mean scores.
Alternate Hypothesis: There is a relation or association among the student’s grade point averages and “if they rather prefer to stay at home than go out with friends”.
Correlations |
| Grade Point Average | I would rather stay at home and read than go out with my friends |
Grade Point Average | Pearson Correlation | 1 | .233 |...

...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 hypothesis testing 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...

...all of the medians are equal.
Step 2 : Step 3 : Step 4 :
Significance Level Rejection Region Reject the nullhypothesis if p-value ≤ 0.05. Test Statistic
α = 0.05
Note that the test statistic (KW = Chi-Square = 7.5023) is corrected for the existence of ties in the ranks of the data.
Step 5 : Step 6 :
Decision Since p-value = 0.0235 ≤ 0.05 = α, we reject the nullhypothesis. State conclusion in words At the α = 0.05...

...Saurabh Sunny Baghmar
MNGT: 6361
Problem Statement: To determine if saving from the total monthly income is gender biased.
Hypothesis: H0: Single Women save equal to single men from their total monthly income. (NullHypothesis)
H0 = µwomen - µmen = 0
Introduction:
The thought behind this problem statement comes from the report which says...