Question

**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 = 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 =/ 0 at the 5% level of
significance?**

Answer #1

Ans

A) since n= 15

Degree of freedom = 14,level of significance = 0.10

Critical value= 1.76

B) the correct p value is lower than the original one .

C)

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

Ans no this not always true.

D)H0 can always be rejected if the observed test statistic is greater than the critical value.

Ans true

E)since the 95%confidence interval = (0.2,0.6)

This interval does not contain zero

So we say that the there is not sufficient evidence to conclude that true mean equal to zero at 5% level of significance.

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...

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...

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...

The following review problem is on hypothesis testing. Could you
please guide on how to approach this?
Suppose one can observe X1, X2, · · · ,
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distribution. For θ0 > 0, we want to test:
H0 : θ = θ0 vs H1 : θ >
θ0.
Use the test statistic Tn = X(n)/ θ0 to
perform a α-level test, where X(n) = max{X1,
X2, · · · , Xn}.
(a)...

Which of the following statements about hypothesis
testing is true?
If the data provide sufficient evidence for the alternative
hypothesis, then the conclusion is to reject H0.
A hypothesis test provides a plausible range of values for a
parameter.
If the data provide sufficient evidence for the null hypothesis,
then the conclusion is to reject H1.
A hypothesis test uses sample data to determine which of two
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For a two-sided hypothesis test in which the test...

You are testing the null hypothesis that there is no linear
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a. What is the value of tSTAT?
b. At the α =0.05 level of significance, what are the critical
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c. Based on your answers to (a) and (b), what statistical
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a. What are the hypotheses to test?
a. H0: ρ ≥0 H1: ρ <0 b. H0:...

A sample is drawn from a population and we estimate that the
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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%.
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PLEASE SHOW WORK
Suppose that in a two-tailed hypothesis test you
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P-value = 0.0802. H0 should be rejected at the 5% level
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A sample of 8 observations from the population indicated that
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H0: σ12 =
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H1: σ12 <
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You should use the tables in the book for obtaining the
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For full marks your answer should be accurate to at least two
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a)
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