Southwestern University Cebu City Graduate School of Health Science, Management and Pedagogy

Statistical Methods (EDUC 201) ACTIVITY 4
HYPOTHESIS-TESTING Instruction: Apply the five steps of hypothesis-testing procedure to each problem below.

1. A researcher conducted an experiment to determine the effect of a lecturer’s age on

student preferences to hear him lecture. In a regular classroom situation, 20 students were told that the administration wished to know their preferences regarding a forthcoming visiting lecturer series. In particular, they were asked to evaluate a professor who “might be visiting the campus.” The professor was described to all students in the same way with one exception: One-half of the students were told the professor was 65 years old: One-half were told the professor was 25 years old. All students were then asked to indicate their willingness to attend the professor’s lecture (higher scores indicates greater willingness). The following results were obtained:

(Scores of the Students Told Professor Was 25 years old)

X1 65 38 52 71 69 72 55 78 56 80

(Scores of Students Told Professor Was 65 years old)

X2 78 42 77 50 65 70 55 51 33 59

Problem 1 X1 = Professor is 25 years old X1 65 38 52 71 (X1)2 4,225 1,444 2,704 5,041 (x1 – x ) 1.4 -25.6 -11.6 7.4 (x1 – x)2 1.96 655.36 134.56 54.76

...HypothesisTesting 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...

...What is HypothesisTesting?
A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesistesting refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.
Statistical Hypotheses
Null hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance.
Alternative hypothesis. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause.
Hypothesis Tests
Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesistesting, consists of four steps.
State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.
Formulate an analysis plan. The analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic.
Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score,...

...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...

...coefficient of correlation, . = 0.076.
a. Compute the coefficient of correlation is .308
b. Determine the coefficient of determination.
Regression Statistics
Multiple R 0.37931016
R Square 0.143876197
Adjusted R Square 0.058263817
Standard Error 15.25058359
Observations 12
The coefficient of determination is 14%.
b. Determine the coefficient of determination is .095
c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.
Yes, there is a positive correlation between the variables.
c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.
Step 1:
Step 2:
The alternative hypothesis is which indicates a one tail test. The degrees of freedom (df) = n-2=12-2=10. The t value at the significance level of .05 and df of 8 and from appendix F is 1.812. The decision rule is to reject the null hypothesis because the test statistic is greater then 1.812.
Step 3:
According to Appendix F, we can assume that P 1.744), there is insufficient evidence to reject the null hypothesis.
P-value Approach: Since the P-value is less than the level of significance of the test, namely (p-value > 0.05), there is insufficient evidence to reject the null hypothesis.
Step 5: Interpret the results.
At the level...

...HYPOTHESISTESTING
WHAT IS THIS HYPOTHESIS????
• In simple words it means a mere assumption or supposition to be proved of disproved.
• But, for a researcher it is a formal question that he intends to resolve.
• Example: I assume that 1) under stress and anxiety a person goes into depression.
2) It leads to aggressive behaviour.
Eg. : Students who get better counselling in a university will show a greater increase in creativity than students who were not counselled.
• So, the hypothesis should be capable of being verified and tested.
CHARACTERISTICS
• Should be clear and precise – inferences not reliable
• Capable of being tested
“ A hypothesis is testable if other deductions can be made from it which, in turn can be confirmed or disproved by observation.”
• Should be limited in scope and must be specific
• Should be stated in simple terms -understandable by all concerned.
• Must explain the facts that gave rise to the need for explanation.
BASIC CONCEPTS: NULL & ALTERNATIVE HYPOTHESIS
• If we are to compare two methods A & B and both are equally good, then this assumption is termed as null hypothesis(H0)
• If it is stated that method A is better than method B-alternative hypothesis(Ha)
LEVEL OF SIGNIFICANCE
• A very important concept in the context of hypothesistesting
• It is represented in a % age...

...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...

...all, the video did a fair job buttressing my understanding of hypothesistesting. The textbook explained the aspects and steps of hypothesistesting in a legible fashion, while the video helped demonstrate a real-life application.
I learned from the text that hypothesistesting is a “Procedure for deciding whether the outcome of a study (results from a sample) supports a particular theory or practical innovation (which is thought to apply to a population)” (Aron A., Aron, E., and Coups, 2011, p. 145). I also learned that hypothesistesting follows a set procedure that appears as follows:
Step 1) Restate the question as a research hypothesis and a null hypothesis about the populations
- Basically, a researcher constructs a hypothesis. Then he/she forms a null hypothesis that opposes the research hypothesis in
polar fashion. To help support one’s research hypothesis, one has to disprove the null hypothesis.
Step 2) Determine the characteristics of the comparison distribution
- When using two or more samples, one must gather information about the distribution of means.
Step 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
- Most researchers...

...Nonparametric HypothesisTesting Paper
ABC’s real estate agency has recently expanded its business and is in the process of conducting research on housing prices within 10 miles of its new office. Team B has been given the task by ABC real estate to conduct the needed research. The team will be able to answer at the end of the research if the prices in Santa Cruz, California, are less than the prices of house in Scott’s Valley, California. Throughout this research process the team will formulate the hypothesis statement, perform a five-step hypothesis test, discuss which nonparametric test was needed, and discuss the results from this data research compare to past research completed.
Five-Step Hypothesis Test
The five-step hypothesis test will determine if consumers have a greater satisfaction when the consumer(s) pay more for the home.
Step one is to state the null hypothesis and alternative hypothesis:
Ho: µ1 = µ2 No difference in satisfaction
Ho: µ1≠ µ2 Satisfaction differs for the two groups
Step two evaluates if the assumptions have been met through the Mann-Whitney test selection that will compare the two populations and will assume equal variances with a 95% confidence level, the significance level is .05. The decision rule is to reject Ho if z>1.645.
Step three the ranks are summed and calculated using the Wilcoxon – Mann-Whitney test....