There are 2 sides to every story. EX. 20% take 12 hours or less versus more than 20% take 12 hours or less.

DEFN. The Alternative Hypothesis is what you want to prove and is labeled HA (because data can disprove the Null Hypothesis which we label H0 )

Q. How many ways can we make a mistake when we draw a conclusion (either support 20% or deduce more than 20%)? P. 396

TRUTH

DECISION = 20% > 20%

I FP
II FN

> 20%

= 20%

TERMINOLOGY

DEFN One-sided Test is a hypothesis testing process where our hypotheses have “less thans” or “greater thans”. Two-sided test has hypotheses of “equal to” and “not equal to”.

EX. Which is ours?

DEFN You find a p-value by asking what’s the probability that the observed sample’s statistic could occur if the sample came from the population described by the null hypothesis.

EX.

Rules of Thumb:

  • if a one-sided test then look at the ‘pointed to’ tail for probability
  • if two-sided then use both tails=probs

The STEP-BY-STEP

  1. Read the problem and form your hypotheses (actually I will give these to you.)
  2. Decide on what and how much to collect and what model the data follows and which statistic you will use to summarize the sample data.
  3. Tell whether the data supports the null or the alternative hypothesis by finding the p-value (you will need a z-score or later a t-score to do this).
  4. State your conclusion in words related to the problem, i.e. either “reject the null hypothesis” or say “data supports the null hypothesis” <Some will talk about the possible errors.>

EXAMPLE

I believe that 20% of Math2200ers take 12 or fewer hours. Let  = Type I = .05? Calculate a p-value; state a conclusion.

1.

HO : p = .20

HA : p > .20

2. we expect p = .20 (mean) with wiggle room of 

so our 11 of 26 (i.e. 11/26) or .42 , does

it seem unusual?

Z = (.42 - .20)/.078 = 2.82

3. 2.82 is big. In fact, p-value is 1-.9976 = .0024 4. .0024<.05 so reject p=.20

DEFN. A p-valueis the probability of getting the observed statistic given the null hypothesis is true.

EX it is the prob I see 11 of 26 if truly only 20% take 12 or fewer hours.

DEFN Results are called statistically significant if our data is unusual enough, i.e. the p-value is smaller than a pre-designated 

(alpha or Type I) error.

EX since I specified and my p-value is like .002 then this means my original data is far away from what is expected or another way to say it is my z-score is big and our results are statistically significant.

Note: .05 is usual…what does it mean? Some researchers use .10 or .01 . This is also called the significance level.

Skip calculating power.

EXAMPLE:

Take a guess at the proportion (percentage) of students at AASU who walk or bike to class.

Set

HO : p = ‘your guess’

HA : p ‘your guess’

State in words what your Type I error would be:

State in words what your Type II error would be:

Fix your(Type I) at .10 or .05 or .01 This means you are willing to take _____ chances in 100 of abandoning your guess when you should not, but you were deceived into doing so because you got misleading data.

How far away from your guess must the data be in order to dissuade you from clinging to it as accurate? (i.e. compute the standard deviation

Do trials by asking the ‘n’ students around you (how many is that?) if they walk or bike. What proportion or percentage do walk or bike?

Is this far from your guess? Answer that by generating a z-score.

Find your p-value by finding the normal tail area and doubling it (due to the not equal in alternative hypothesis).

Is p-value < ? Is your z-score big? Is your data collected far from your guess?

What do you conclude about the data supporting your guess? About rejecting your guess?

1