Stats 2 tips

F test notes

posted Dec 3, 2010, 7:07 PM by Prof Kiernan   [ updated Dec 3, 2010, 7:39 PM ]

You can use the F test to verify a claim about a standard deviation (or variance) for 2 data sets.

Assumptions: The sample is from a "normal distribution"

NOTE: some professors prefer to use the following notation: N~(mean, Standard Deviation)

English Translation: Use an F test  if you are Given: 2 sample sizes (n) and 2 standard deviations (or variances=s2 ) AND you are testing a claim about a standard deviation or variance.

Writing the hypothesis:

H0population standard deviation1 = population standard deviation2

H1: population standard deviationis less than, greater than, or not equal to population standard deviation2

Critical Value = shaded area from F table using the degrees of freedom.

Degrees of freedom: for numerator (use the info from the bigger Standard Deviation) n-1, for denominator (use the info from the smaller Standard Deviation) n-1. Remember that if the null hypothesis requires two tails, split the alpha before using the tables.

Test statistic formula:

F = variance1 / variance2

**The bigger variance (standard deviation squared) must be divided by the smaller variance (standard deviation squared).**


Press STAT

Highlight TESTS

Select 2-SampFTest 

Put your information in.

    **NOTE: S1 must be the biggest standard deviation**

Make sure the not equal to, less than, or greater than symbol matches the one in your alternative hypothesis (H1).

Highlight Calculate Press ENTER

F is the test statistic, and P is the P-value.

Rejection of the null hypothesis (Ho):

You can reject the null hypothesis if:

  • the F from the formula falls in the shaded critical area from the table.
  • the P-value is smaller than your alpha Reject Ho.

Remember: if you are not given an alpha assume you are using 0.05.

A little fun with the Ftest

posted Dec 3, 2010, 7:02 PM by Prof Kiernan   [ updated Dec 3, 2010, 7:07 PM ]

I stumbled across this comic and thought you might find it amusing especially if you're struggling with Hypothesis testing and the ANOVA (analysis of variance).

Hypothesis testing workshop

posted Oct 7, 2010, 1:38 PM by Prof Kiernan

Hi everyone,
There will be a workshop on hypothesis testing on Thursday OCT 21,2010 from 2:30 to 3:30 in the IRC Room 116.
Click here to RSVP for a seat and free candy.
If the link doesn't work try this one:

Confidence intervals

posted Sep 15, 2010, 1:46 PM by Prof Kiernan

Welcome back, the first sections of Stats 2 will cover a review of stats one and an introduction to the confidence interval. Not only is it important that you understand how to create a confidence interval but you must be able to translate their meaning from stats into everyday english. In short, a confidence interval is found via a formula and states that within a certain amount of error (E) you can be certain that your data should fall between two numbers.

I've attached an example of how to create a confidence interval.



Happy summer everyone!

posted Aug 10, 2010, 7:56 AM by Prof Kiernan   [ updated Aug 12, 2010, 11:18 AM ]

Happy summer everyone!
Heads up, this is the material you need to remember if you're planning on starting Stats 2 this semester.

Review descriptive statistics, basic graphs (histogram, box plot, stem & leaf, cumulative frequency polygon), normal curve, central limit theorem. Might want to also do assessing normality (section 6-2).

Which formula to use:

posted Feb 19, 2010, 7:59 AM by Prof Kiernan

parameter Conditions/given Confidence Interval
test statistic Key words
Proportion nP > 5 & nQ < 5

population proportion (P)

sample proportion
(p = x/n)

q=1-p & Q=1-P



You are not given a standard deviation
Mean population data known
n > 30

σ (population standard deviation)
population mean (μ)         _
sample mean: X
sample size = n
You know what the population standard deviation is.
Mean population data NOT known
and n < 30

s (sample standard deviation)
population mean (μ)         _
sample mean: X
sample size = n
Given sample info
Standard deviation
OR variance(σ²)
Population normally distributed
σ (population standard deviation)
sample size = n
s (sample standard deviation) 

You're working with a hypothesis
about the standard
deviation of a sample

Population or Sample

posted Oct 23, 2009, 12:21 AM by Unknown user   [ updated Feb 4, 2010, 5:39 AM by Prof Kiernan ]

"Samples are small, & they're written in English

Populations are general, & they're written in Greek."

    All sample (portions of the whole group) data is written using english letters. Whereas, the majority of population data use Greek notation. 

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