QM - F - T-test

Question 1

It is a statistical test procedure that tests whether there is a significant difference between the means of two groups.​

Answer 1

t-Test

Question 2

is a tool for evaluating the means of one or two populations using hypothesis testing.

Answer 2

t-Test​

Question 3

may be used to evaluate whether a single group differs from a known value (a one-sample t-test), whether two groups differ from each other (an independent two-sample t-test), or whether there is a significant difference in paired measurements (a paired, or dependent samples t-test).

• Population’s Standard Deviation is unknown

Answer 3

t-Test

Question 4

Synonyms of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 4

One-Sample t-test
* Student’s t-test

Two-Sample t-test
* independent groups/samples t-test
* equal variances t-test
* pooled t-test
* unequal variance t-test

Paired t-test
* paired group t-test
* dependent samples t-test

Question 5

# of Variables of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 5

One-Sample t-test
* one

Two-Sample t-test
* two

Paired t-test
* two

Question 6

Types of Variables of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 6

One-Sample t-test
* Continuous measurement

Two-Sample t-test
* Continuous measurement
* Categorical or Nominal to define groups

Paired t-test
* Continuous measurement
* Categorical or Nominal to define pairing within group

Question 7

Purpose of Test of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 7

One-Sample t-test
* Decide if the population mean is equal to a specific value or not.
* Compare the mean of the sample to the mean of a known reference value.

Two-Sample t-test
* Decide if the population means for two different (independent) groups are equal or not

Paired t-test
* Decide if the difference between paired (dependent) measurements for a population is zero or not. Usually the sample data is taken before and after the intervention

Question 8

Example: Test if… of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 8

One-Sample t-test
* Mean heart rate of a group of people is equal to 65 or not

Two-Sample t-test
* Mean heart rates for two groups of people are the same or not
Paired t-test
* Mean difference in heart rate for a group of people before and after exercise is zero or not

Question 9

Estimate of Population Mean of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 9

One-Sample t-test
* sample average

Two-Sample t-test
* sample average for each group

Paired t-test
* sample average of the differences in paired measurements

Question 10

Population Standard Deviation of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 10

One-Sample t-test
* Unknown, use sample standard deviation

Two-Sample t-test
* Unknown, use sample standard deviations for each group

Paired t-test
* Unknown, use sample standard deviation of differences in paired measurements

Question 11

Degrees of Freedom of ONE-, TWO-SAMPLE & PAIRED T-TEST

Answer 11

One-Sample t-test
* Number of observations in sample minus 1, or: n–1

Two-Sample t-test
* Sum of observations in each sample minus 2, or: n1 + n2 – 2

Paired t-test
* Number of paired observations in sample minus 1, or: n–1

Question 12

examines whether the mean of a population is statistically different from a known or hypothesized value.
* is a parametric test

Answer 12

One Sample t-Test

Question 13

also known as Single Sample t Test
* he variable used in this test is known as Test variable

Answer 13

One Sample t-Test

Question 14

the test variable’s mean is compared against a “test value”, which is a known or hypothesized value of the mean in the population. Test values may come from a literature review, a trusted research organization, legal requirements, or industry standards.​

Answer 14

One Sample t-Test

Question 15

The null hypothesis (H0) and (two-tailed) alternative hypothesis (H1) of the one sample T test can be expressed as:​

H0: µ = µ0 (“the population mean is equal to the [proposed] population mean”)​
H1: µ ≠ µ0 (“the population mean is not equal to the [proposed] population mean”)​

where µ is the “true” population mean and µ0 is the proposed value of the population mean. ​

Answer 15

Hypothesis

Question 16

NULL vs ALTERNATIVE HYPOTHESIS

Answer 16

NULL
* Ho
* is a statistical hypothesis that contains a statement of equality such as
<, =, >.
ALTERNATIVE
* Ha
* is a statement that must be true if Ho is fales and contains a statement of inequality such as >, !=, <

Question 17

• the alternative hypothesis contains the less-than inequality symbol (<)

Answer 17

left-tailed

Question 18

• the alternative hypothesis contains the greater-than inequality symbol (>)

Answer 18

right-tailed

Question 19

• the alternative hypothesis contains the not-equal-to symbol (≠)

Answer 19

TWO-TAILED

Question 20

is used when the alternative hypothesis specifies a direction (e.g., less than or greater than the claimed mean).​

Answer 20

ONE TAILED TEST

Question 21

Example Hypotheses:​

𝐻0:μ≥μ0​ , 𝐻𝑎:μ<μ0​ (left-tailed test)​

𝐻0:𝜇≤𝜇0, 𝐻𝑎:μ>μ0​ (right-tailed test)

Answer 21

ONE TAILED TEST

Question 22

Is used when the alternative hypothesis does not specify a direction, and you are testing for a difference in either direction. (Testing for equality, reject, difference)​

Answer 22

TWO-TAILED TEST

Question 23

Example Hypotheses:​

𝐻0:𝜇=𝜇​, 𝐻𝑎:𝜇≠𝜇0 (mean is different from the claimed value)

Answer 23

ONE TAILED TEST