Case: Statistics in Action: Diary of a Kleenex User (graded)
Hypothesis Testing
Class: Our goal with hypothesis testing is to determine if a claim regarding a population may be
correct. The answer to this question depends on many factors, such as: 1) the sample size, 2)
the sample parameter, and 3) the variability of the sample.
Let's look at an example. If an instructor believes s/he has a better way to teach statistics and
measures success on final exam test scores, we can use hypothesis testing to test if the "better
way to teach statistics" really is "better." There must be some historical baseline information
from which the instructor wishes to improve. Let's say that using the past 5 years of data, in
which there really has been very little change in the teaching methods, the final exam scores
have averaged 75 with a standard deviation of 3 points. With the newer methods, a sample of
15 students is taken and shows final exam scores are higher on average, let's say 80. Have the
newer methods used really shown improvement relative to the student's ability to perform well
on the final exam?
*** IMPORTANT ***
In the example above, we will set up two hypothesis: the null hypothesis and the alternate
hypothesis. Now…….. (key point here)……. we always think the alternate hypothesis is correct!
We use Ho to represent the null hypothesis and Ha to represent the alternate hypothesis. Let
“mu” equal the true mean of all statistics students on the final exam, which is actually the
population mean. We think, based upon the sample of 15 students, that the population mean is
now above 75. (Why? The sample mean is 80… which is above 75!)
So, Ho is “mu <= 75” and Ha is “mu > 75”. Remember that we always think the alternate
hypothesis is correct.
Now, we need to figure out which one of these hypotheses is correct. We will assume the null
hypothesis is correct and we’ll try to reach a conclusion that we should reject that assumption.
That is, we will try to reject the null hypothesis. That means that we accept the alternate
hypothesis, which is what we thought was correct at the very beginning!!!!
This study source was downloaded by 100000829957125 from CourseHero.com on 01-18-2022 10:31:40 GMT -06:00
https://www.coursehero.com/file/11196222/MATH-533-GM-533-Week-5-Discussion/
, We will use a confidence level equal to 1- alpha to help us determine how far above 75 our
sample mean needs to be in order to determine that the true population mean is above 75.
Remember that we have a sample that suggests the mean is greater than 75, but the sample is
not the actual population. The sample mean is 80 and we’re not sure that 5 point difference is
definite. If we take another sample, that sample will undoubtedly have a different sample mean.
If we took a third sample, it would undoubtedly have a sample mean different from the first two.
So, based upon our one sample, how far about 75 must the sample mean be for us to decide
that the true population mean is above 75? That’s the purpose of hypothesis testing.
Hypothesis testing provides us with a series of specific steps that lets us conclude which
hypothesis is correct.
1st Step: Determine the null and alternate hypothesis. (We always think the alternate is correct.)
2nd Step: Determine the “rejection region” based upon alpha and the hypothesis from Step 1. If
the alternate hypothesis is “not equal to” we have a two-tailed rejection region. If the alternate
hypothesis is “less than” we have a left-tailed rejection region. If the alternate hypothesis is
“greater than” we have a right-tailed rejection region.
3rd Step: Calculate the test statistic based upon the data obtained from the sample.
4th Step: Make a decision using the test statistic from step 3 with conditions in step 2.
5th Step: Summarize decision in terms of “English” and not statistical speak!!
What are the null and alternative hypotheses in this (Kleenex Tissues) case? Be sure to use Ho and Ha
notation.
The null hypothesis also referred to as Ho, will yield the acceptable results unless the
information given is incorrect. The alternate, or Ha, hypothesis will be accepted if the
information provided has evidence to support and back it up. The exercise this week asks us to
take a look at the Kimberly-Clark Corporation’s Kleenex Survey (of a total of 250 people).
From the information that I have gathered and worked with, it has been determined that mean
for Ho Notion (Null Hypothesis) is less than 60.
Kleenex Survey:
N=250
Mean=56.76
This study source was downloaded by 100000829957125 from CourseHero.com on 01-18-2022 10:31:40 GMT -06:00
https://www.coursehero.com/file/11196222/MATH-533-GM-533-Week-5-Discussion/
Hypothesis Testing
Class: Our goal with hypothesis testing is to determine if a claim regarding a population may be
correct. The answer to this question depends on many factors, such as: 1) the sample size, 2)
the sample parameter, and 3) the variability of the sample.
Let's look at an example. If an instructor believes s/he has a better way to teach statistics and
measures success on final exam test scores, we can use hypothesis testing to test if the "better
way to teach statistics" really is "better." There must be some historical baseline information
from which the instructor wishes to improve. Let's say that using the past 5 years of data, in
which there really has been very little change in the teaching methods, the final exam scores
have averaged 75 with a standard deviation of 3 points. With the newer methods, a sample of
15 students is taken and shows final exam scores are higher on average, let's say 80. Have the
newer methods used really shown improvement relative to the student's ability to perform well
on the final exam?
*** IMPORTANT ***
In the example above, we will set up two hypothesis: the null hypothesis and the alternate
hypothesis. Now…….. (key point here)……. we always think the alternate hypothesis is correct!
We use Ho to represent the null hypothesis and Ha to represent the alternate hypothesis. Let
“mu” equal the true mean of all statistics students on the final exam, which is actually the
population mean. We think, based upon the sample of 15 students, that the population mean is
now above 75. (Why? The sample mean is 80… which is above 75!)
So, Ho is “mu <= 75” and Ha is “mu > 75”. Remember that we always think the alternate
hypothesis is correct.
Now, we need to figure out which one of these hypotheses is correct. We will assume the null
hypothesis is correct and we’ll try to reach a conclusion that we should reject that assumption.
That is, we will try to reject the null hypothesis. That means that we accept the alternate
hypothesis, which is what we thought was correct at the very beginning!!!!
This study source was downloaded by 100000829957125 from CourseHero.com on 01-18-2022 10:31:40 GMT -06:00
https://www.coursehero.com/file/11196222/MATH-533-GM-533-Week-5-Discussion/
, We will use a confidence level equal to 1- alpha to help us determine how far above 75 our
sample mean needs to be in order to determine that the true population mean is above 75.
Remember that we have a sample that suggests the mean is greater than 75, but the sample is
not the actual population. The sample mean is 80 and we’re not sure that 5 point difference is
definite. If we take another sample, that sample will undoubtedly have a different sample mean.
If we took a third sample, it would undoubtedly have a sample mean different from the first two.
So, based upon our one sample, how far about 75 must the sample mean be for us to decide
that the true population mean is above 75? That’s the purpose of hypothesis testing.
Hypothesis testing provides us with a series of specific steps that lets us conclude which
hypothesis is correct.
1st Step: Determine the null and alternate hypothesis. (We always think the alternate is correct.)
2nd Step: Determine the “rejection region” based upon alpha and the hypothesis from Step 1. If
the alternate hypothesis is “not equal to” we have a two-tailed rejection region. If the alternate
hypothesis is “less than” we have a left-tailed rejection region. If the alternate hypothesis is
“greater than” we have a right-tailed rejection region.
3rd Step: Calculate the test statistic based upon the data obtained from the sample.
4th Step: Make a decision using the test statistic from step 3 with conditions in step 2.
5th Step: Summarize decision in terms of “English” and not statistical speak!!
What are the null and alternative hypotheses in this (Kleenex Tissues) case? Be sure to use Ho and Ha
notation.
The null hypothesis also referred to as Ho, will yield the acceptable results unless the
information given is incorrect. The alternate, or Ha, hypothesis will be accepted if the
information provided has evidence to support and back it up. The exercise this week asks us to
take a look at the Kimberly-Clark Corporation’s Kleenex Survey (of a total of 250 people).
From the information that I have gathered and worked with, it has been determined that mean
for Ho Notion (Null Hypothesis) is less than 60.
Kleenex Survey:
N=250
Mean=56.76
This study source was downloaded by 100000829957125 from CourseHero.com on 01-18-2022 10:31:40 GMT -06:00
https://www.coursehero.com/file/11196222/MATH-533-GM-533-Week-5-Discussion/
