LAB 1: Hypothesis Testing and Statistical Analysis

Question 1

Science is a formalized process for testing tentative ideas called___________, which must be stated so
that they have the potential to be proven false

Answer 1

hypotheses

Question 2

Hypotheses that are repeatedly tested and inferred to be true may be integrated with other similar ‘true’
hypotheses and be elevated to the status of a _____.

Answer 2

theory

Question 3

The Research Hypothesis

Answer 3

Research hypotheses are the outgrowth of observation and inquiry. A researcher may observe an
interesting phenomenon and wonder why it has occurred. After asking questions and consulting other
sources this initial observation is refined into a research hypothesis and an experimental procedure that
will test its validity. A research problem is not a legitimate area of scientific inquiry if a testable
hypothesis cannot be formulated. For example, the idea that demons are responsible for a person’s
actions is not testable by experimentation

Question 4

The Statistical Hypotheses

Answer 4

Statistical hypotheses are an outgrowth of the research hypothesis and are statements about particular
data samples. There are two statistical hypotheses made concerning a data sample; the null hypothesis
and the alternative hypothesis. Both of these hypotheses must be stated in order to conduct a statistical

Question 5

Null hypothesis

Answer 5

The null hypothesis states that there is no difference or no effect and it is the null hypothesis that is
tested in a statistical procedure

Question 6

Mean or Average:

Answer 6

The most frequently used measure to characterize a population is the arithmetic mean (or average). The mean is an expression of the ‘central tendency’ of a population:
Where is the mean, X1 , X2 , etc. are individual measurements, and n is the total number of
measurements.
mean = (X1 + X 2 + X 3 + etc) / n

Question 7

Variance symbol

Answer 7

s^2

Question 8

The________ is one way to measure the degree of variability within a population.

Answer 8

variance

Question 9

large variance indicates that the individual scores deviate ___________ from the
mean, whereas a small variance indicates that the scores deviate _________ from the mean

Answer 9

considerably
very little

Question 10

What is the equation for variance?

Answer 10

s^2 = ∑ (Xi − X)^2 / (n − 1)
-To calculate the variance of a sample population, the
mean is subtracted from each of the individual observations. The deviations from the mean are
then squared, summed, and divided by the number of observations minus 1 (n - 1). Although we
will not pursue this here, statisticians have determined that using n - 1 gives an unbiased estimate
of a sample population variance but division by n does not.

Question 11

Normal Distribution:

Answer 11

A population with a bell-shaped distribution of values about its mean is said to have a “normal”
distribution.
- on a graph it would look like a roller coaster going up and then down

Question 12

standard deviation symbol

Answer 12

S

Question 13

Equation for standard deviation

Answer 13

The standard deviation (S) is calculated by taking the square root of the variance:
S=√s^2

Question 14

Standard Error symbol

Answer 14

SE

Question 15

Standard error equation

Answer 15

SE= s / √s^2

Question 16

What is standard error for?

Answer 16

indicates how different the population mean is likely to be from a sample mean.
-small sample sizes and high variances yield means with large standard
errors, whereas large sample sizes and low variances yield means with small standard errors. In other words, the more samples you collect from a population, and the closer those measurements are to the sample mean, the lower the error of your estimate of the population mean will be

Question 17

A __________ __________ is used to confirm that the difference between sample means is
significant; that is, that the difference in the means is real and not due to chance events.

Answer 17

statistical test

Question 18

null hypothesis

Answer 18

which assumes that there will be
no difference as a result of experimental treatment. If we find evidence to the contrary, we reject
the null hypothesis and conclude that the noted difference probably did not result from chance
alone.

Question 19

There are several statistical tests that can help us determine if the difference between two
sample means is significant. One of the most common is the _______ _ _______

Answer 19

student’s t-test

Question 20

The t- test includes what three steps?

Answer 20

-First, the test statistic “t” is calculated.
-Second, a critical t value is determined.
-Third, the calculated t value is compared to the critical t value.
The relationship between these t values determines whether two means are significantly different

Question 21

What is the first step of calculation a t- test? t stat

Answer 21

STEP 1: Calculate the test statistic “t” as follows:
“t”= X1 - X2 / √(s^2 1/n1)+(s^2 2/n2)
- X1 = mean of sample 1, X2 =mean of sample 2
- n1 = # of data points (observations) in sample 1,
- n 2 = # of data points (observations) in sample 2
s^2 1 = variance of sample 1, s^2 2 = variance of sample 2

Question 22

Step two of calculating a t- test? degrees of freedom equation

Answer 22

df = n 1 + n2 -2
where n1 = sample size of group 1,
and n 2 = sample size of group 2

Question 23

Degrees of freedom symbol

Answer 23

df

Question 24

p-value

Answer 24

is the probability of making a
Type I error (i.e., falsely rejecting a true null hypothesis)

Question 25

(Alfa)a=_____

Answer 25

0.05
-then the researcher is willing to accept at maximum a 5% chance of making a Type I error

Question 26

Where do you find critical t value?

Answer 26

you find it in a table given where a is set to 0.05 and degrees of freedom(df) is your sample sizes minus 2

Question 27

Step three of calculating a t-test: compare calculated t and critical t

Answer 27

Decision Rule: If t calc ≤ t crit … then accept the null hypothesis (reject the alternative
hypothesis), the means are not significantly different.

If t calc > t crit … then reject the null hypothesis, the means are significantly different. You would accept the alternative hypothesis if it is non-directional (two-sided), or if it is directional (one-sided) and the means differ in the
hypothesized direction

Question 28

Using the p-value to determine significance:

Answer 28

If p > α (e.g., 0.05), accept the null hypothesis, the means are not significantly different.

If p < α (e.g., 0.05), reject the null hypothesis, the means are significantly different.