Question

True or False

1. Hypothesis tests are robust to the significance level you choose, meaning regardless of the alpha level: .10, .05, or .01, our test will have the same conclusion or result.

2. If alpha is greater than the p-value, then we reject the null hypothesis.

3. The p-value is strictly the probability the null hypothesis being true.

4. Hypothesis tests are accessing the evidence provided by the data and deciding between two competing hypotheses about the population parameter.

5. When the alternative hypothesis is saying that the parameter is different than the hypothesized value, we have a two-sided test.

Answer #1

1. **False**. For example, for n=30 and population
standard deviation is unknown, some time we use large sample test
i.e. Z test instead of t test when our parameter of interest is
population mean. In that situation, we can get different
conclusions for given alpha. This is also observed in other large
sample and exact tests. Moreover this scenario is also found in non
parametric tests (for example sign test and Wilcoxon sign rank
test).

2. **True**.

3. **False**, since p-value is the probability of
obtaining results as extreme as the observed results of a
statistical hypothesis test, when the null hypothesis is true.

4. **True**.

5. **True**.

You perform a hypothesis test for a hypothesized population mean
at the 0.01 level of significance. Your null hypothesis for the
two-sided test is that the true population mean is equal to your
hypothesized mean. The two-sided p-value for that test is 0.023.
Based on that p-value... A. you should accept the null hypothesis.
B. the null hypothesis cannot be correct. C. you should reject the
null hypothesis. D. you should fail to reject the null
hypothesis.

True or False: The higher the level of significance of a
hypothesis test, the stronger the evidence we require to reject the
null hypothesis.
True or False: The purpose of a hypothesis test is to assess the
evidence in favour of the null hypothesis.
True or False: The higher the p-value of a hypothesis test, the
more evidence we have to reject the null hypothesis.

True or False: The higher the level of significance of a
hypothesis test, the stronger the evidence we require to reject the
null hypothesis.
True or False: The purpose of a hypothesis test is to assess the
evidence in favour of the null hypothesis.
True or False: The higher the p-value of a hypothesis test, the
more evidence we have to reject the null hypothesis.

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 _____....

True or False: For all hypothesis tests, a small p-value means
we will reject the null.
True or False: If you are testing the means of two groups, then
you would use ANOVA.
True or False: A two-sample confidence interval must capture
zero to show the groups are different.
True or False: The test statistic for ANOVA is the
f-statistic.
True or False: For Chi-Square tests, if the observed counts and
expected counts are extremely different, then we would have...

The p-value is the same as alpha, the level of significance of
the hypothesis test.
True
False

Large Sample Proportion Problem. A survey was
conducted on high school marijuana use. Of the 2266 high school
students surveyed, 970 admitted to smoking marijuana at least
once. A study done 10 years earlier estimated that 45%
of the students had tried marijuana. We want to conduct a
hypothesis test to see if the true proportion of high school
students who tried marijuana is now less than 45%. Use
alpha = .01.
What is the conclusion for this test?
Group of...

In a two-tailed hypothesis test of the mean using a 0.05 level
of significance, researchers calculated a p-value of 0.03. What
conclusion can be drawn? The alternative hypothesis should be
rejected because the p-value is so small. The null hypothesis is
true because the p-value is less than the level of significance.
The alternative hypothesis is 3% likely to be true. The null
hypothesis should be rejected because the p-value is less than the
level of significance.
1.The alternative hypothesis...

You perform 3800 significance tests using a significance level
of 6%. Assuming that the null hypothesis is true, how many of the
test results would you expect to be statistically significant?
Please show working for the problem.

Suppose that before we conduct a hypothesis test we pick a
significance level of ?. When the test is conducted, we get a
p-value of 0.023. Given this p-value, we
a. can reject the null hypothesis for any significance level, ?,
greater than 0.023.
b. cannot reject the null hypothesis for a significance level,
?, greater than 0.023.
c. can reject the null hypothesis for a significance level, ?,
less than 0.023.
d. draw no conclusion about the null hypothesis.

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