Three teaching methods were tested on a group of 19 students with homogeneous backgrounds in statistics and comparable aptitudes. Each student was randomly assigned to a method and at the end of a 6-week program was given a standardized exam. Because of classroom space and group size, the students were not equally allocated to each method. The results are shown in the table below. Test for a difference in distributions (medians) of the test scores for the different teaching methods using the Kruskal-Wallis test. Method 1 94 87 90 74 86 97 Method 2 82 85 79 84 61 72 80 Method 3 89 68 72 76 69 65 1. Enter the time values into one variable and the corresponding teaching method number (1 for Method 1, 2 for Method 2, 3 for Method 3) into another variable (see figure, below). Be sure to code your variables appropriately.

2.

Select Graphs Boxplot… (Simple, Summaries for groups of cases) with the variable measured (Test Score) and the category axis variable (Teaching Method) entered (see figures, below). Click “OK”.

3.

Your resulting side-by-side boxplots will appear (see figure, below). As long as the boxes have approximately the same shape, you may continue with the ANOVA procedure.

4.

Select Analyze

Nonparametric Tests

K Independent Samples… (see figure, below).

5.

Select “Test Score” as the test variable, select “Teaching Method” as the grouping factor, and click “Define Range…”. Enter the minimum value (1) and the maximum value (3). Click “Continue” to close the range definitions and then 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)....

...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...

...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...

...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...

...Simple Hypothesis: A statisticalhypothesis 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 statisticalhypothesis 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.
HypothesisTesting or Test of Hypothesis or Test of Significance
HypothesisTesting 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...

...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...

...deviation is 12. Using the five steps of hypothesistesting and the 5% significance level (i.e. alpha = .05), does showing the film change students’ attitudes towards the chronically mentally ill?
What does it mean to set alpha at .05?
Alpha means making a Type I error same as significance level. When the alpha is at .05 it means that the researcher doesn’t want to take a big risk therefore sets the alpha to .05. By doing this it will make it hard forhypothesistesting process to reject the null hypothesis unless it is extreme.
α=0.05 means: P (type I error) = 0.05, rejecting Ho being Ho true is 0.05
What is your null hypothesis? And Alternate hypothesis?
The null hypothesis would be that watching films on institutionalization will change students’ attitudes about chronically mentally ill patients. The Alternative Hypothesis would be that watching films on institutionalization will not change students’ attitudes about chronically mentally ill patients.
Ho: μ=75 (Null)
Ha: μ≠ 75 (Alternate)
Is this a one-tailed or two-tailed hypothesis?
The hypothesis is two-tailed since we are using a significance level of 0.05. Therefore, no matter the direction you are hypothesizing the researcher is testing for the possibility on both sides since the alternative is: Ha: μ≠ 75 it is two-tailed
What is...

...questionnaire for these 36 students is 70. The score for people in general on this questionnaire is 75, with a standard deviation of 12. Using the five steps of hypothesistesting and the 5% significance level (i.e. alpha = .05), does showing the film change students’ attitudes towards the chronically mentally ill?
•
What does it mean to set alpha at .05? Alpha at .05 means there is a .05 probability or 5% chance of committing a Type I error, which means that we have rejected our null hypothesis and found support for our alternate hypothesis when, in fact, the null hypothesis was true.
•
What is your null hypothesis? Alternate hypothesis? Ho : mean of group 1 = mean of group 2 Ha : mean of group 1 ≠ mean of group 2
•
Is this a one-tailed or two-tailed hypothesis? This is a two-tailed test since no direction is predicted (e.g. “will change” attitudes).
•
What is the criterion z? zcrit. = -1.96 This is found by using the z table in the textbook. Since it is a two-tailed test, alpha of .05 is split between the two tails. Thus the critical z is ± 1.96, so for our example, we would use -1.96.
•
Suppose the obtained z was -2.5. Do you reject or fail to reject the null hypothesis? Our obtained z value of -2.5 is more extreme (in this case smaller) than our criterionz of -1.96. We reject the null hypothesis.
•
State in...

...4. Hypothesistesting
The main aim of the module is to familiarize students with the theoretical knowledge of hypothesistesting and then train them in applying theory to economic practice.
After completing this module, students will be familiar with:
the procedure of hypothesistesting;
the possible outcomes in hypothesistesting;
the difference between significant and nonsignificant statistical findings.
After completing this module, students will be able to:
define what is meant by a hypothesis and hypothesistesting;
understand the logic of hypothesistesting and describe the steps of hypothesistesting procedure;
determine the appropriate hypothesis test to perform;
formulate and write the null and alternative hypotheses;
understand the meaning of the significance level and distinguish between a one-tailed and a twotailed test;
test hypotheses about a population mean;
state conclusions to hypothesis tests.
4.1. Introduction to hypothesistesting
A hypothesis is a statement about the value of a population parameter.
The population of interest is so large that for various reasons it would not be feasible to study all the...

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