1.6 Tests Concerning a Single Mean

Question 1

what is a t-test commonly used for?

Answer 1

commonly used to test the value of an underlying population mean

The t-distribution is similar to the standard normal distribution, but it is impacted by the degrees of freedom

Smaller degrees of freedom produce fatter tails

Question 2

The z-test can be used for what?

Answer 2

be used for a large sample, even if the population variance is unknown

Question 3

when do the t and z-test as the nyumber of observations increases?

Answer 3

when the sample size increases

Question 4

a z-test rejection point of z0.10 is equal to what?

Answer 4

1.28

Question 5

a z-test rejection point of z0.05 is equal to what?

Answer 5

1.645

Question 6

a z-test rejection point of z0.025 is equal to what?

Answer 6

1.96

Question 7

a z-test rejection point of z0.01 is equal to what?

Answer 7

2.33

Question 8

a z-test rejection point of z0.005 is equal to what?

Answer 8

2.575

Question 9

First way (two-sided test):

Answer 9

H0: u1 - u2 = 0
Ha: u1 - u2 =/= 0

Question 10

Second way (one-sided test):

Answer 10

H0: u1 - u2 <= 0
Ha: u1 - u2 > 0

Question 11

Third way (one-sided test):

Answer 11

H0: u1 - u2 => 0
Ha: u1 - u2 < 0

Question 12

A paired comparison test

Answer 12

a statistical test for differences in dependent items

The difference between two random variables taken from dependent samples, denoted di, is calculated. Then, the list of differences is statistically analyzed.

Question 13

First way (two-sided test)

Paired comparison test

Answer 13

H0: ud = udo

Ha: ud =/= ud0

Question 14

second way (one-sided test)

Paired comparison test

Answer 14

Ho: ud <= ud0

Ha: ud > ud0

Question 15

third way (one-sided test)

Paired comparison test

Answer 15

Ho: ud => ud0

Ha: ud < ud0

Question 16

Other than the population mean, analysts are also often interested in performing hypothesis tests on the population variance.

what can we use for this?

Answer 16

Chi-square test

can be used to test the relationship between an observed sample variance and its hypothesized value

Question 17

Chi-square test

First way (two-sided test)

Answer 17

H0: σ^2 = σ0^2

Ha: σ^2 =/= σ0^2

Question 18

Chi-square test

second way (one-sided test)

Answer 18

H0: σ^2 <= σ0^2

Ha: σ^2 > σ0^2

Question 19

Chi-square test

third way (one-sided test)

Answer 19

H0: σ^2 => σ0^2

Ha: σ^2 < σ0^2

Question 20

why do we use the F-test?

Answer 20

to examine the equality/inequality of two population variances

The F test is used based on the ratio of the sample variances.

The F-distribution is bounded below by 0 and defined by two values of degrees of freedom–for the numerator and for the denominator

Question 21

F test

First way (two-sided test)

Answer 21

H0: σ1^2 = σ2^2

Ha: σ1^2 =/= σ2^2

Question 22

F test

second way (one-sided test)

Answer 22

H0: σ1^2 <= σ2^2

Ha: σ1^2 > σ2^2

Question 23

F test

third way (one-sided test)

Answer 23

H0: σ1^2 => σ2^2

Ha: σ1^2 < σ2^2

Question 24

a parametric test

Answer 24

The hypothesis testing procedures that deal with parameters and are dependent on assumptions

Parametric tests are better for precise conclusions but are limited due to the underlying assumptions

Question 25

a nonparametric test

Answer 25

not concerned with parameters or makes minimal assumptions on the underlying population

Question 26

Nonparametric procedures are used when:

Answer 26

1. The data do not meet distributional assumptions
2. The data are subject to outliers
3. The data are given in ranks or use an ordinal scale
4. The hypotheses do not concern a parameter.

Question 27

correlation coefficient

Answer 27

measure of strength between variables

Question 28

If there is no linear relationship between the two variables, the correlation coefficient will be

Answer 28

0

Question 29

Assuming the correlation coefficient is denoted p:

First-way (two sided-test)

Answer 29

H0: p = 0

Ha: p =/= 0

Question 30

Assuming the correlation coefficient is denoted p:

second way (one-sided-test)

Answer 30

H0: p <= 0

Ha: p > 0

Question 31

Assuming the correlation coefficient is denoted p:

third way (one-sided-test)

Answer 31

H0: p => 0

Ha: p < 0

Question 32

The parametric correlation coefficient (a.k.a. the Pearson correlation or bivariate correlation) of two variables can be tested based on what?

Answer 32

the sample correlation

Question 33

A sample is taken from a normally distributed population with known variance. The observations in this sample are sorted according to an ordinal scale. To test a hypothesis regarding the sample mean, an analyst would most likely use a:

A
t-test.

B
z-test.

C
nonparametric test.

Answer 33

C
nonparametric test.

Question 33

The Spearman rank correlation coefficient

Answer 33

similar to the correlation coefficient but does not rely on the same underlying assumptions

Question 34

the standardized residual (a.k.a. Pearson residual

Answer 34

cells that have observations that deviate significantly from their expectations.