Question

**PROVIDING STEPS:**

(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 ƒ= 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 = 0 vs H1 : µ > 0. The test statistic, 1.31, was found to be wrongly calculated. The correct test statistic should be 2.31 instead. Is the correct p-value higher than, lower than, or the same as the original one?

(c) Suppose we are performing a hypothesis test and we conclude that we can reject H0 at the 10% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance?

(d) Determine if the following statement is true or false: H0 can always be rejected if the observed test statistic is greater than the critical value.

(e) Based on the data, we obtain (0.2, 0.6) as the 95% confidence interval for the true mean. What can we say about the test with the hypotheses H0 : µ = 0 against H1 : µ ƒ= 0 at the 5% level of significance?

Answer #1

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...

Question 3 This question concerns some concepts about
hypothesis testing and confidence interval. For each part below,
you must explain your answer.
(a) Suppose we are doing a one-sample t test at the 5% level of
significance where the hypotheses are H0 : µ = 0 vs H1 : µ > 0.
The number of observations is 8. What is the critical value? [2
marks]
(b) Suppose we are doing a hypothesis test and we can reject H0
at the...

A sample is drawn from a population and we estimate that the
two-sided 99% conﬁdence interval on the mean of the population is
1.09007 ≤ µ ≤ 1.40993. One of the following statement is correct,
determine which.
A. We would reject the null hypothesis H0 : µ = 1.1 against the
alternative hypothesis H1 : µ 6= 1.1 at the level of signiﬁcance α
= 1%.
B. We would fail to reject the null hypothesis H0 : µ = 1.5...

A sample of 8 observations from the population indicated that
sample variance s12 is 784. A second sample
of 8 observations from the same population indicated that sample
variance s22 is 144. Conduct the following
test of hypothesis using a 0.05 significance level.
H0: σ12 =
σ22
H1: σ12 <
σ22
You should use the tables in the book for obtaining the
F values.
For full marks your answer should be accurate to at least two
decimal places.
a)
State...

A sample of 6 observations from the population indicated that
sample variance s12 is 529. A second sample
of 5 observations from the same population indicated that sample
variance s22 is 256. Conduct the following
test of hypothesis using a 0.1 significance level.
H0: σ12 =
σ22
H1: σ12 ≠
σ22
You should use the tables in the book for obtaining the
F values.
For full marks your answer should be accurate to at least two
decimal places.
a)
State...

We want to test H0 : µ ≤ 120 versus Ha : µ > 120 . We know
that n = 324, x = 121.100 and, σ = 9. We want to test H0 at the .05
level of significance. For this problem, round your answers to 3
digits after the decimal point.
1. What is the value of the test statistic?
2. What is the critical value for this test?
3. Using the critical value, do we reject or...

PLEASE SHOW WORK
Suppose that in a two-tailed hypothesis test you
calculated a Z statistic of -1.75. What is your p-value? And how
would you conclude if α = 5%?
P-value = 0.0401. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should be rejected at the 5% level
P-value = 0.0802. H0 should not be rejected at the 5% level
P-value = 0.0402. H0 should be rejected at the 5% level
None of the above...

Suppose we observe Y1,...Yn from a normal distribution with
unknown parameters such that ¯ Y = 24, s2 = 36, and n = 15.
(a) Find the rejection region of a level α = 0.05 test of H0 : µ
= 20 vs. H1 : µ 6= 20. Would this test reject with the given
data?
(b) Find the rejection region of a level α = 0.05 test of H0 : µ
≤ 20 vs. H1 : µ > 20....

A sample of 42 observations has a mean of 103 and a population
standard deviation of 7. A second sample of 61 has a mean of 100
and a population standard deviation of 9. Conduct a z-test
about a difference in sample means using a 0.04 significance level
and the following hypotheses:
H0: μ1 -
μ2 = 0
H1: μ1 - μ2 ≠
0
a)
What is the correct decision rule?
Reject H0 in
favour of H1 if the computed...

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...

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