Question

A
hypothesis test for a population mean is to be performed. True or
False: The probability of a Type I error is equal to the
significance level.

Answer #1

**Solution**

The statement is **True**.

Let us discuss this in detail,

**Type I error :** It is an error occured when the
rejection of null hypothesis when it is true. That is the null
hypothesis is actually true but we reject it. Or we can say that
error occured when we accept the alternative hypothesis when the
null hypothesis is true. This kind of error is called Type I
error.

And **Significance level is the probability of rejecting
the null hypothesis when it is true.** It is same as the
probability or Type I error.

**Hence we can say that the probability of Type I error is
equal to the significance level .** That is our given
statement is TRUE.

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If p = 0.62, find the
probability of making a type II error, β.
Fill in the blanks below to
describe the sampling distribution of ??� assuming H0 is
true.
Mean =
Standard deviation =
Shape:
Sketch the sampling distribution
of ??�assuming H0 is true.
Specify the rejection region...

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If = 0.62, find the
probability of making a type II error, β.

A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If p = 0.62, find the
probability of making a type II error, β.
Answer:
A. Fill in the
blanks below to describe the sampling distribution of ??� assuming
H0 is true.
Mean:
Standard
deviation:
Shape:
Sketch the sampling distribution of ??� assuming H0 is
true.
B. Specify...

A hypothesis test is to be performed with a Null hypothesis
Ho: µ ≥ 15 and an alternative
hypothesis H1: µ <
15, the population standard deviation
is σ=2.0, the sample size is;
n=50, and the significance level is
α=0.025.
1- What is type l error?
2- What is the chance of making a type I error in the above
test?
3- What is a Type II error?
4- What value would the sample mean have to be less than to...

Question 1 (1 point)
True or False:
The power of a test is the probability of rejecting the null
hypothesis when the null is false.
Question 1 options:
True
False
Question 2 (1 point)
What type of error occurs when a false null hypothesis is not
rejected?
Question 2 options:
Type I
Type II
Type III
Rejection Error
Question 3 (1 point)
Which type of error results in a "false alarm?"
Question 3 options:
Type I
Type II
Type III...

1. The P-value of a test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is false, that
the test statistic will take a value at least as extreme as that
actually observed.
d. the probability, assuming the null hypothesis is true, that
the test statistic will take a value at least as extreme as that
actually observed.
2. The P-value...

We have a left tail one sample test for the population mean.
Assume the null hypothesis is true. Use 4% for the significance
level. The sample size is 27, the sample mean is 32.8, the sample
standard deviation is 4.1, and the null mean is 35.
The test result is (a) a correct decision (b) a Type I error (c)
a Type II error 3.
The test statistic value for the previous problem is

1 The probability of type II error becomes bigger if the level
of significance is changed from 0.01 to 0.05.
True
False
2
Increasing the sample size reduces the probability of committing
a Type I and Type II simultaneously.
True
False
3
In testing a hypothesis about a population mean with an unknown
population standard deviation (σ ) the degrees of freedom
is used in the denominator of the test statistic.
True
False
4
When a researcher fails to reject...

We have a one sample test for the population mean. The
significance level is a fixed value. Suppose we increase the sample
size. Assume the true mean equals the null mean.
(a) The t critical value moves closer to zero.
(b) The size of the rejection region decreases
(c) The probability of a Type I error decreases
(d) The probability of a Type I error increases

. Consider the following hypothesis test: H0 : µ ≥ 20 H1 : µ
< 20 A sample of 40 observations has a sample mean of 19.4. The
population standard deviation is known to equal 2. (a) Test this
hypothesis using the critical value approach, with significance
level α = 0.01. (b) Suppose we repeat the test with a new
significance level α ∗ > 0.01. For each of the following
quantities, comment on whether it will change, and if...

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