Simple Hypothesis: A statistical hypothesis which specifies the population completely (i.e. the form of probability distribution and all parameters are known) is called a simple hypothesis. 1. Composite Hypothesis: A statistical hypothesis which does not specify the population completely (i.e. either the form of probability distribution or some parameters remain unknown) is called a Composite Hypothesis.

Hypothesis Testing or Test of Hypothesis or Test of Significance Hypothesis Testing is a process of making a decision on whether to accept or reject an assumption about the population parameter on the basis of sample information at a given level of significance.

Null Hypothesis: Null hypothesis is the assumption which we wish to test and whose validity is tested for possible rejection on the basis of sample information.

It asserts that there is no significant difference between the sample statistic (e.g. Mean, Standard Deviation(S), and Proportion of sample (p)) and population parameter (e.g. Mean(µ), standard deviation (σ), Proportion of Population (P)).

Symbol-It is denoted by Ho

Acceptance- The acceptance of null hypothesis implies that we have no evidence to believe otherwise and indicates that the difference is not significant. Rejection- The rejection of null hypothesis implies that it is false and indicates that the difference is significant.

Alternative Hypothesis: Alternative hypothesis is the hypothesis which differs from the null hypothesis. It is not tested. Symbol-It is denoted by H1.
Acceptance- its acceptance depends on the rejection of the null hypothesis. Rejection- Its rejection depends on the acceptance of the null hypothesis.

Level of Significance

Level of significance is the maximum probability of rejection the null hypothesis when it is true.

Symbol- it is usually expressed as % and is denoted by symbol α (called Alpha) Example- 5% level of significance implies that there are about 5 chances in...

...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...

...Given 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 null hypothesis, 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 corresponding p-value of the hypothesis test?
7. (12 points) What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, representatives of AFP would like to have the conclusion skewed to their advantage. And so would 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...

...CHAPTER 4 – THE BASIS OF STATISTICALTESTING
* samples and populations
* population – everyone in a specified target group rather than a specific region
* sample – a selection of individuals from the population
* sampling
* simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research
* extremely difficult, time-consuming, expensive
* cluster sampling – identify clustering units in the population
* opportunity sampling – selecting participants who just happen to be available at the time and the place that you are conducting your research
* snowball sampling – referrals from participants
* volunteer sampling – where you might advertise your study and wait for people who have read your ad to come forward to take part
* how generalizable are data?
* Q: are the means for our sample approximately equal to the mean from the population?
* randomly selected sample because of this random factor, sample may not be exactly representative
* sampling error
* the difference between the sample mean and the population mean
* ensure that you have enough participants so that you get an accurate reflection of the population that you are interested in
* population mean (parameter), sample mean (statistic)
* the larger the...

...Business Statistics, 9e (Groebner/Shannon/Fry)
Chapter 10 Estimation and HypothesisTesting for Two Population Parameters
1) The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. If the sample size is n = 10 from each population, the samples are independent, and sample standard deviations are used, and the variances are assumed equal, then the critical value will be t = 2.1009.
Answer: TRUE
Diff: 2
Keywords: confidence interval, mean difference, independent, sample
Section: 10-1 Estimation for Two Population Means Using Independent Samples
Outcome: 1
2) To find a confidence interval for the difference between the means of independent samples, when the variances are unknown but assumed equal, the sample sizes of the two groups must be the same.
Answer: FALSE
Diff: 2
Keywords: confidence interval, mean difference, independent
Section: 10-1 Estimation for Two Population Means Using Independent Samples
Outcome: 1
3) The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. Assume that the variances are equal and the populations normally distributed. The following data represent independent samples from each...

...click “OK”. (See the 3 figures, below.)
6.
Your output should look like this.
7.
You should use the output information in the following manner to answer the question.
Step 0 : Check Assumptions The samples were taken randomly and independently of each other. The populations have approximately the same shapes (according to the boxplots). All sample sizes are at least 6 if k = 3 (smallest is 6). Hypotheses
Step 1 :
H0 : M1 = M2 = M3 (The median test scores are equal.) Ha : Not all of the medians are equal.
Step 2 : Step 3 : Step 4 :
Significance Level Rejection Region Reject the null hypothesis 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 null hypothesis. State conclusion in words At the α = 0.05 level of significance, there exists enough evidence to conclude that there is a difference among the three teaching methods based on the test scores.
...

...HypothesisTesting: Alzheimer's Disease
Natalie Sullivan
PSY/315
August 8, 2011
Deborah Suzzane Ph.D.
HypothesisTesting: Alzheimer's Disease
One in eight American’s over age 65 are diagnosed with Alzheimer’s disease. This number continues to grow as the population increases. The number of people affected by Alzheimer’s is alarming. The Alzheimer’s Association (2011) estimates that 5.4 million Americans of all ages suffer from this disease. Team A will attempt to form a hypothesis stating that the number of Alzheimer’s diagnoses will statistically increase each year at an alarming rate. We will then test our hypothesis based on data collected and provide our recommendation.
Alzheimer’s is the most common form of dementia that causes problems with the memory, thinking, and behavior. Dementia is caused by various diseases and conditions that result in damaged brain cells or connections between brain cells. The earliest signs of Alzheimer’s are difficulty remembering names and recent events. Apathy and depression are also early signs. Eventually, an Alzheimer’s patient will experience impaired judgment, disorientation, confusion, behavior changes, and difficulty speaking, swallowing, and walking. The causes of Alzheimer’s remain unknown. The majority of the Alzheimer’s diagnoses take place in men and women over the age of 65; however, young people can develop this disease...

...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)
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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.
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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...