Question

2. What is the size of a test? What is the power of a test?

Answer #1

Solution:

**What is the size of a test?**

The size of the test is the probability of committing type I error. i.e. The probability of rejecting the null hypothesis when it is true.

In testing of hypothesis theory , there are two types of errors:

Type I error: Rejecting the null hypothesis when it is true.

Type II error : Fail to reject the null hypothesis when it is False

The size of the test is also known as "Significance level".

It is denoted by a Greek letter .

**What is the power of a test?**

"Rejecting the Null hypothesis when it is False" is the correct decision.

The power of test is the probability of "Rejecting the Null hypothesis when it is False"

The power of the test is given by

power = 1 -P(Fail to reject the null hypothesis when it is False)

= 1 - P(Type II error)

= 1 -

What is the approximate power associated with a sample
size of 61 when used to detect a population correlationthat is
equal to .04 with a .01, one tailed test?
.13
.22
.78
.87

What is the approximate power associated with a sample size of
61 when used to detect a population correlationthat is equal to .04
with a .01, one tailed test?
.13
.22
.78
.87

Which of the following is correct about the power of the test?
Check all that apply. a. As alpha increases, power decreases. b. As
standard error decreases, power increases. c. As Type I error
increases, power increases. d. As effect size increases, power
increases. e. As sample size increases, power increases. f. As
sample size increases, power is unaffected. g. As Type II error
decreases, power decreases.

The easiest way to affect the outcome of a hypothesis test is
to increase sample size. Similarly, true results may sometimes be
missed because a sufficient sample was not used in the research.
Perform the hypothesis test on these data with a sample of 37. Then
perform the same hypothesis test but assume that the mean was based
on only 4 infants.
The easiest way to increase statistical power is to increase
sample size. Similarly, statistical power decreases with a...

Power and sample size determination for one-way ANOVA 1. If µ1 =
12, µ2 = 13, µ3 = 18 and µ4 = 21 with s e = 5, what is the power of
the test when n1 = 2, n2 = 3, n3 = 3 and n4 = 2 and a = .05? 2. If
µ1 = 12, µ2 = 13, µ3 = 18 and µ4 = 21 with s e = 5, what is the
power of the test...

Several factors influence statistical power for a one-sample t
test. How does statistical power change (increase or decrease) for
each of the following changes? When d (effect size) increases. When
N (sample size) increases. When the alpha level is made smaller.
Explain your answer. For example, if we know ahead of time that the
effect size d is very small, what does this tell us about the N we
will need in order to have adequate statistical power? (We assume...

If the probability of a type II error in a hypothesis test is
0.07, what is the power of the hypothesis test? Assuming your
sample is unbiased, would increasing the size of the sample
increase or decrease the power of the hypothesis test? Please
explain your answer.

What effect does increasing sample size have on power, beta, and
alpha? For each, state why.

Describe the relationships between power, effect size, and
sample size. How do researchers usually increase their sample
size.

Statistical power analysis seeks to optimize the size of the
___________.
difference
sample
population
correlation
Statistical power is the likelihood that an effect will be
detected in the sample when one ____________.
is hypothesized to exist
has been found in previous research
really exists
exists in a previous sample of the same population
The probability of failing to detect an effect when one exists
is known as a _______.
Type I error
Type II error
Power
Standardized error
Which of...

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