Question

How does the 95% confidence interval correspond to the reported conclusion at a 0.05 significance level?

The confidence interval contains the value of ‘0’, and the results of the test were statistically significant.

The confidence interval contains the value of ‘0’, and the results of the test were not statistically significant.

The confidence interval does not contain the value of ‘0’, and the results of the test were statistically significant.

The confidence interval does not contain the value of ‘0’, and the results of the test were not statistically significant.

Answer #1

The hypothesis test is statistically significant. If the confidence interval does not contain the null hypothesis value, the results are statistically significant.

if Confidence level does not contains null hypothesis value,we reject null hypothesis hence results are statistically significant

if we failed to reject H0, results are not significant

The confidence interval contains the value of ‘0’, and the results of the test were not statistically significant.

The confidence interval does not contain the value of ‘0’, and the results of the test were statistically significant.

A 96% confidence interval for the mean is reported as (0.8, 2.3)
for a set of data. Suppose we want to conduct a two-sided
significance test with the null hypothesis Ho: μ = 0
using the computed confidence interval.
1) What level of significance would be used in the test of
significance ?
2) Are the results statistically significant? Fully justify
why/why not.

Significane Level of a=0.05 is used for each hypothesis
test and a confidence level of 95% is used for each confidence
interval estimate.
A random sample of people who work regular 9-5 hours and a
random sample of people who work shifts were asked how many hours
of sleep they get per day on average. An appropriate F-Test was
performed and it was found that the null hypothesis of the F-Test
should be rejected. Can we infer that there is...

In the following exercise, use a significance level of α = 0.05
to
State a conclusion about the null hypothesis. (Reject
H0 or fail to reject H0 )
Without using technical terms or symbols, state a conclusion
that addresses the original claim.
Original Claim: More than 58% of adults would erase all their
personal information online if they could. The hypothesis test
results in a P-value of 0.3257.

Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
include negative and positive numbers.
No. Increasing the confidence level leads to...

Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
A. Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
include negative and positive numbers.
B.
No. Increasing the confidence level...

On the basis of this test, what is your conclusion, assuming the
significance level is = 0.05? Is the mean platelet yield greater
than 3.9 x 10? Is the Amicus machine more efficient than the other
machine?
One-Sample
Statistics
N
Mean
Std. Deviation
Std. Error Mean
Platelet Yield
16
4.0063
.50394
.12599
One-Sample
Test
Test Value = 3.9
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence
Interval of the Difference
Lower
Upper
Platelet Yield
.843
15
.412
.10625
-.1623
.3748

The 95% confidence interval for the difference in proportions
between sample 1 and same 2 is approx.
(-0.006, 0.286). What is the appropriate conclusion?
Is the difference significant, highly significant or
insignificant at the 5% significance level.

Please criticize the following statement regarding the
interpretation of a confidence interval:
Results for a 95% Confidence Interval for estimating the
population mean: 74.1< Mean< 83.1
" After looking at the above results we can conclude that there
is a 95% chance that the confidence interval contains the true mean
of the population"
Is the above statement correct? Why? If it is not correct how
can we re-state the conclusion in order to interpret correctly the
above confidence interval?

9.12 Suppose a 95% confidence interval for p1−p2 is (0.43,
0.51). A researcher wants to test H0∶p1−p2=0.5 versus Ha∶p1−p2≠0.5
at α=0.05 significance level. What is the p−value for this
test?

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.

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