Question

1. In testing a null hypothesis H0 versus an alternative Ha, H0 is ALWAYS rejected if

A. at least one sample observation falls in the non-rejection region.

B. the test statistic value is less than the critical value.

C. p-value ≥ α where α is the level of significance. 1

D. p-value < α where α is the level of significance.

2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0, suppose Z be a test statistic and z0 be the observed value of Z from the sample. At significance level α, let zα be the critical value. It was observed that z0 < zα. What would be your conclusion?

A. H0 is rejected since there is sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

B. H0 is accepted since there is sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

C. Failed to reject H0 since there isn’t sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

D. H0 is rejected since there isn’t sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

3. For a test H0 : µ = 0 vs H0 : µ 6= 0 with test statistic T and value of the test statistic 1.36, what would be the appropriate p-value?

A. P(T > 1.36) B. P(T < 1.36) C. 0.05 D. 2 ∗ P(T > 1.36)

4. A Type II error is

A. rejection of null hypothesis H0 when, in fact, it is false.

B. failing to reject of null hypothesis H0 when, in fact, it is false.

C. rejection of null hypothesis H0 when, in fact, it is true.

D. failing to reject of null hypothesis H0 when, in fact, it is true.

Answer #1

**1. In testing a null hypothesis H0 versus an alternative
Ha, H0 is ALWAYS rejected if**

Ans. *p-value < α where α is
the level of significance.*

**2. In testing a null hypothesis H0 : µ = 0 vs Ha : µ
> 0, suppose Z be a test statistic and z0 be the observed value
of Z from the sample. At significance level α, let zα be the
critical value. It was observed that z0 < zα. What would be your
conclusion?**

Ans. *Failed to reject H0 since
there isn’t sufficient sample evidence with level α that the true
value of the population mean µ is greater than 0.*

**3. For a test H0 : µ = 0 vs Ha : µ
0 with test statistic T and value of the test statistic 1.36, what
would be the appropriate p-value?**

Ans. *2 ∗ P(T >
1.36)*

**4. A Type II error is**

Ans. *failing to reject of null
hypothesis H0 when, in fact, it is false.*

1. Which statement is incorrect?
A. The null hypothesis contains the equality sign
B. When a false null hypothesis is not rejected, a Type II error
has occurred
C. If the null hypothesis is rejected, it is concluded that the
alternative hypothesis is true
D. If we reject the null hypothesis, we cannot commit Type I
error
2. When carrying out a large sample test of H0: μ ≤ 10
vs. Ha: μ > 10 by using a critical value...

1.For testing H0 : p = 0.5 vs. Ha : p < 0.5 at level α, let a
sample of size n = 100 is taken. What would be an appropriate
rejection region?
A. t0 < tα B. z0 < zα C. z0 > zα D. |z0| > zα/2
2. A test statistic
A. is a function of a random sample used to test a hypothesis.
B. is a function of a parameter used to test a hypothesis. C. is...

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

1.) Choose the true statement.
a.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
never reject.
b.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
always reject.
c.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it may or
may not reject.
2.)...

Suppose that in a certain hypothesis test the null hypothesis is
rejected at the .10 level; it is also rejected at the .05 level;
however it cannot be rejected at the .01 level. The most accurate
statement that can be made about the p-value for this test is
that:
p-value = 0.01.
p-value = 0.10.
0.01 < p-value < 0.05.
0.05 < p-value < 0.10.
Complete the sentence: If we do not reject the null hypothesis,
we conclude that _____....

Consider the following hypothesis test.
H0: p = 0.30
Ha: p ≠ 0.30
A sample of 500 provided a sample proportion
p = 0.275.
(a)
Compute the value of the test statistic. (Round your answer to
two decimal places.)
(b)
What is the p-value? (Round your answer to four decimal
places.)
p-value =
(c)
At
α = 0.05,
what is your conclusion?
Do not reject H0. There is sufficient
evidence to conclude that p ≠ 0.30.Do not reject
H0. There...

Consider the following hypothesis test.
H0: p = 0.20
Ha: p ≠ 0.20
A sample of 400 provided a sample proportion
p = 0.185.
(a)
Compute the value of the test statistic. (Round your answer to
two decimal places.)
(b)
What is the p-value? (Round your answer to four decimal
places.)
p-value =
(c)
At
α = 0.05,
what is your conclusion?
Do not reject H0. There is sufficient
evidence to conclude that p ≠ 0.20.Reject
H0. There is sufficient...

Q2. This question is testing your understanding of some
important concepts about hypothesis testing and confidence
intervals. For each part below, you must explain your
answer.
(a) Suppose we are performing a one-sample t test at the
10% level of significance where the
hypotheses are H0 : µ = 0 vs H1 : µ =/ 0. The number of
observations is 15. What is the critical value?
(b) Suppose we are performing a one-sample t test with
H0 : µ...

Consider the following hypothesis test.
H0: μ ≤ 12
Ha: μ > 12
A sample of 25 provided a sample mean x = 14
and a sample standard deviation s = 4.65.
(a) Compute the value of the test statistic. (Round your answer
to three decimal places.)
(b) Use the t distribution table to compute a range for
the p-value.
a. p-value > 0.200
b. 0.100 < p-value <
0.200
c. 0.050 < p-value < 0.100
d. 0.025 < p-value...

Consider the following hypothesis test.
H0: μ ≤ 12
Ha: μ > 12
A sample of 25 provided a sample mean x = 14 and a sample
standard deviation s = 4.64.
(a)
Compute the value of the test statistic. (Round your answer to
three decimal places.)
(b)
Use the t distribution table to compute a range for the
p-value.
p-value > 0.2000.100 < p-value <
0.200 0.050 < p-value <
0.1000.025 < p-value < 0.0500.010 <
p-value < 0.025p-value <...

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