Question

11. The correct interpretation of 95% confidence is (Circle
one):

a) We can be 95% confident that the interval includes the sample
mean.

b) 95% of all possible population means will be included in the
interval.

c) 95% of the possible sample means will be included in this
interval.

d) The method used to get the interval, when used over and over,
produces intervals which include the true population mean 95% of
the time.

12. Suppose a two-sided (or two-tailed) alternative hypothesis
has been set up, and the test statistic is found to be z = 1.1.
What will the p-value be?

a) 0.8643

b) 0.2714

c) 0.1357

d) 0.0250

e) 0.0500

13. I conduct a hypothesis test and reject the null hypothesis
at a significance level of .05. Based only on this information, I
may conclude that

a) I would also reject the null hypothesis if the alpha level was
.10 rather than .05.

b) I would also reject the null hypothesis if the alpha level was
.01 rather than .05

c) both (a) and (b) are true.

d) Cannot be determined from the given information.

Answer #1

11) interpretation of confidence interval is

The method used to get the interval, when used over and over, produces intervals which include the true population mean 95% of the time.

Option D is correct

12) we have Z = 1.1 and two tailed test

P-value = 2 * P( Z > 1.1)

p-value = 0.2714

13) Decision rule : if p-value < a , we reject the null hypothesis , otherwise we fail to reject the null hypothesis

Here if we reject the null hypothesis at 0.05 level of significance then we also reject the null hypothesis at 0.10

Answer is I would also reject the null hypothesis if the alpha level was .10 rather than .05.

Option a) is correct

Select the correct answer for the following two questions:
1.The length of a 95% confidence interval is _____ the length of
a 90% confidence interval
A. longer than
B. equal
C. shorter than
D. half
2. if a p-value for a hypothesis test = 0.02, that means that
approximately ___ of the time, we will correctly fail to reject a
true null hypothesis.
A. 2%
B. 98%
C. 95%
D. 5%

The 95% confidence interval for the population mean was
calculated based on a random sample with sample size of n=31 as (50
to 60). Calculate the outcome of a 2 sided alpha=0.05 test based on
the null hypothesis of H0: mean=55, and determine if:
A.We would reject the null hypothesis.
B. We would accept the null hypothesis.
C. We woudl fail to reject the null hypothesis.
D. Not enough information to decide.

Question 1.
Which of the following is the CORRECT interpretation of a 95%
confidence interval?
a) There is a 95% probability that the interval contains the
population value
b) There is a 95% chance that the true population value is
inside the interval
c) if we sampled from a population repeatedly and created
confidence intervals, 95% of those confidence intervals would
contain the population mean
d) We are 95% sure of the sample statistic
Question 2.
What is the mean...

An estimated regression coefficient is equal to 0.5. What is the
confidence level associated with the one sided interval(0.5,∞)?
a. 50%
b. 95%
c. 100%
d. 90%
Suppose a hypothesized slope value is not contained in the 95%
confidence interval. If one were test the hypothesis at the 10%
level which of the following statements are correct?
a. I would reject the null hypothesis
b. I would not reject the null hypothesis
c. I need more information
Suppose the value...

The 95% confidence interval is functionally equivalent to:
A) non-directional hypothesis testing with a 0.05 alpha
level.
B) an interval based on a directional test with a 2.5% chance of
Type I Error.
C) the acceptable amount of Type I Error.
D) an inferential test with a 5% chance of Type II Error.
E) the likelihood of rejecting a false null 2.5% of the
time.

1a. Suppose the value a is inside the 90% confidence interval
for a coefficient in an estimated regression. Suppose one were to
test the hypothesis that the coefficient is equal to a against the
two sided alternative that it is not equal to a. Which of the
following is a correct statement?
I would not reject the null at the 10% significance level
I would reject the null hypothesis at the 5% level of
significance
I would reject the null...

a. We are testing H0: μ1 - μ2 =
0. Our 95% confidence interval is (-23.95,-7.41).
We should expect the t-statistic to be _____( greater than 2
/between 0 and 2/ between 0 and -2 /less than -2) .
We should expect the p-value to be _______ (less than .05/
greater than .05/ equal to .05).
We should ______(reject /fail to reject) H0
and conclude that the group 1 population average is _____(smaller/
larger) than the group 2 population average.
It...

Using techniques from an earlier section, we can find a
confidence interval for μd. Consider a
random sample of n matched data pairs A,
B. Let d = B − A be a random
variable representing the difference between the values in a
matched data pair. Compute the sample mean
d
of the differences and the sample standard deviation
sd. If d has a normal distribution or
is mound-shaped, or if n ≥ 30, then a confidence
interval for μd...

1. A 95% CI for a population mean is 44.1±4.88
.(a) Can you reject the null hypothesis that ?=37 at
the 5% level? (Type: YES or NO or CANNOT TELL):
(b) Can you reject the null hypothesis that ?=48 at the
5% level? (Type: YES or NO or CANNOT TELL):
(c) In general, you fail to reject the null hypothesis if
? is the confidence interval. (Type: IN or NOT IN) :
2 . A random sample of size ?...

Suppose I estimate μ, the mean of a population. I obtain
estimate 6.5 and 95% confidence interval (4.5, 8.5).
A) Can I reject H0 : μ = 8 using at two-sided test at the 1%
significance level?
a) Yes.
b) No.
c) Not enough information to decide.
B) Can I reject H0 : μ = 8 using at two-sided test at the 1%
significance level?
a) Yes.
b) No.
c) Not enough information to decide.
C) Can I reject H0...

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