Single Sample Hypothesis Test
How do we know it is a single-sample hypothesis test?
There is a benchmark value and 2 population groups.
What is step 1 in hypothesis testing?
Stating your null hypothesis (both verbal and symbolic)
What is our chosen alpha?
a=.05
The data we are using is collected from a nationally representative random sample of lesbian, gay, and bisexual individuals. We have collected a random sample of data from around 1400 LGBT individual concerning their economic strain and their perceived health. To begin we want to know whether the EconomicStrain(measured as a summed variable ranging from 0 to 12) of LGBT folks is different than the benchmark for the EconomicStrain of Americans (μAmericans = 4.25)?
What is the benchmark value?
4.25
Please come to the front and state the outline of the symbolic and verbal version of a null hypothesis.
H0=MuPopulation1 = MuPopulation 2 OR
H0=MuPopulation1 = Benchmark
There is no difference between [pop. 2] and [pop. 1] in terms of [variable of interest]
What is step 2 in hypothesis testing?
Stating the alternative hypothesis (both verbal and symbolic)
What are the assumptions of a z-test?
1. Observations are independent of one another
2. A random sample
3. Populations data are normally distributed
4. Population variance is known
The data we are using is collected from a nationally representative random sample of lesbian, gay, and bisexual individuals. We have collected a random sample of data from around 1400 LGBT individual concerning their economic strain and their perceived health. To begin we want to know whether the EconomicStrain(measured as a summed variable ranging from 0 to 12) of LGBT folks is different than the benchmark for the EconomicStrain of Americans (μAmericans = 4.25)?
What kind of test are we doing?
Single Sample T-Test
Please come to the front and state the outline of the symbolic and verbal version of the alternative hypothesis.
Symbolic:
HA: Mupopulation2 ≠ Mupopulation1 OR
HA: Mupopulation2 ≠ Benchmark Value
HA: There is a difference between [population 2] and [population 1] in terms of [variable of interest].
What is the 3rd step in hypothesis testing?
Choosing our test statistic.
When do we fail to reject the null hypothesis?
If our p-value is greater than our chosen alpha of a=.05
We randomly tested 3000 high school students in a California school district for height in 2023. We want to know how the high school students in Nevada school district compared in 2025. The benchmark for this test is approximately 64 inches tall.
What kind of test are we doing?
Single Sample Hypothesis Test
What are the assumptions?
1. Independent Observations
2. Random Sampling
3. Normally Distributed Population Data
What is step 4 in hypothesis testing?
Determining whether we meet the assumptions for the specified test.
What is a null hypothesis telling us?
That nothing happens, nobody's different, and nothing ever changes.
•In 2023 the national survey of health attitudes collected information on the health attitudes and beliefs from approximately 7100 randomly selected Americans. One of the variables in this survey asks Americans how important religion is to them. Answer classes for this variable are on a 5-point Likert scale anchored by 1(not at all important) to 5(very important). In 1985 a random sample of Americans determined that the average American had an importance of religion score of 4.01. you want to know whether our 2023 sample is different than the u.s. in 1985.
How would we write an alternative hypothesis both verbally and symbolically?
HA: Mu2023 ≠ Mu1985 OR
HA: Mu2023 ≠ 4.01
There is a difference between Americans in 2023 and Americans in 1985 in terms of religious importance.
What is the outline of the conclusion if we rejected the null hypothesis?
"Our sample of [insert sample description] has a test statistic of z= [z-score], with a p-value of p= [p-value]. Since our p-value is less than our chosen alpha of a = .05. We will reject our null hypothesis that states [insert null] and find support for our research hypothesis that states [alternative hypothesis]."
What is step 5 in hypothesis testing? Please specify the outline.
Writing the test statistic:
t(df)= t-value, p-value
What is a hypothesis?
Educated Guess
It allows scientists to turn a problem statement into something testable.
The data we are using is collected from a nationally representative random sample of lesbian, gay, and bisexual individuals. We have collected a random sample of data from around 1400 LGBT individual concerning their economic strain and their perceived health. To begin we want to know whether the EconomicStrain(measured as a summed variable ranging from 0 to 12) of LGBT folks is different than the benchmark for the EconomicStrain of Americans (μAmericans = 4.25)?
What is the null hypothesis verbally and symbolically?
H0: MuLGBT = MuAmericans OR
H0: MuLGBT = 4.25
There is no difference between LGBT folks and American folks in terms of economic strain.