Download 10.16 and 10.18 DPS Notes - b

Psych 101 Chapter 12 Notes: 10/16 & 10/18
-We will be comparing the population parameter to the a statistic (the entire population
compared to a select few that we hope are representative of the whole population)
-We know the statisctic and population parameter aren’t always going to be the same
thing
-sampling error: the difference between a sample statistic and the corresponding
population parameter as a result of chance during sampling’
-The Central Limit Theorem states:
 Sampling distribution of the mean has the shape of the normal curve
 Sampling distribution has the same mean as the population mean
 Standard Deviation or Standard Error of the sampling distribution is equal to the
population standard deviation divided by the square root of the sample size
Hypothesis Testing: assessing the probability of getting your actual sample statistic,
given a hypothesized population parameter
4 STEPS OF HYPOTHESIS
TESTING
Step 1: Define the null and alternative hypotheses about
the population.
Step 2: Draw a random sample from the population, and
calculate the statistic of interest (e.g., the mean)
Step 3: Describe the sampling distribution of the statistic,
given the null hypothesized population parameter and
sample size
Step 4: Determine the cutoff value (Critical z) on the
sampling distribution, place the calculated z-score on
the sampling distribution, and decide whether to reject
or retain the null hypothesis
STEP 1. DEFINE NULL AND ALTERNATE HYPOTHESES
Null hypothesis: a specific statement about a
population parameter made for the purposes of
argument.
Alternate hypothesis: represents all other possible
parameter values except that stated in the null hypothesis.
The alternate is typically the one the researcher wants to
show.
Our hypotheses are ALWAYS about the actual population even thought we’re
getting our information from the sample
Ho-null hypothesis
Ha-alternate hypothesis
With Ho:
-we can either reject or fail to reject (retain) Ho
With Ha:
-it is the hypothesis that the researcher hopes is true
-p-value: the actual probability of drawing your sample from the null hypothesized
population
-Statistical Significance: a maximum acceptable probability that we use to reject the null
hypothesis when it is true
If a sample mean is so different from what is expected when
H0 is true that it would be so unlikely to have occurred by
chance, reject H. Otherwise, do not reject H.
-usually the significance level is 0.05
-When p is less than or equal to our a(significance level), we reject the null hypothesis
-most tests are 2-tailed tests, meaning that a deviation in EITHER direction would reject
the null hypothesis
Statistically significant?
p<a
We can “reject the null hypothesis”
Not significant
p>a
We “fail to reject the null hypothesis”
-we can never prove or accept the null hypothesis!
ASSUMPTIONS OF Z-TESTS
1. A random sample has been drawn from the population.
2. The sample was drawn with replacement.
3. The sampling distribution of the mean is normal
(Which means you have interval or ratio data).
• The Central Limit theorem tells us this will happen if
we have a normal distribution in the population, or
if we have a sample of 30 or more.
4. The standard deviation of the population is known.
-the further the sample mean is from the population mean, the more likely you are able to
reject the null hypothesis
-So far, we have been assuming that we know the population standard deviation, but if
we don’t, we would use the following formula
Sx=square root(sum of x- sample mean)^2/n)
-a sample standard deviation, which is what we get from the formula above, provides a
biased estimate of the corresponding population standard deviation AND is more than
likely to underestimate true variability in the population than to overestimate BUT if we
use the equation listed above and divide by n-1 instead of n, it would be more unbiased
-Instead of a z-score, we would use a t-score when we DON’T know the population
standard deviation
-How is a t-score different from a z-score?
 Shape of a t distribution is very similar to the normal curve BUT it’s a little flatter
at the top and heavier in the tails
 -difference between t-test and z-test is more prominent in smaller samples
-we also specify df (degrees of freedom) when we use a t-test