Question

1. TRUE or FALSE State whether the statement is true or false, and also give a brief sentence explaining why you believe this.

(a) If we decrease the confidence level for a fixed n, we decrease the width of the confidence interval.

(b) A research article reports that a 95% confidence interval for mean reaction time is from 0.25 to 0.29 seconds. About 95% of individuals will have reaction times in this interval.

c) In a hypothesis test, a p-value of 0.035 is observed. This means we would reject the null hypothesis at a significance level of α = 0.01.

d)If a null hypothesis is rejected at a 0.01 significance level, it will also be rejected at a 0.05 significance level.

(e) If the test statistic falls outside of the rejection region, the null hypothesis has been proven to be true.

(f) A 95% confidence interval for a population mean µ is calculated to be (20.16, 20.42). If a test of H0 : µ = 20.1 against Ha : µ 6= 20.1 is conducted at a significance level of α = 0.05 using the same sample, the decision would be to retain H0.

Answer #1

1.) Choose the true statement.
a.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
never reject.
b.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it would
always reject.
c.) If a null hypothesis is rejected for a test statistic at the
α=0.05 level, then at the α=0.01 level it may or
may not reject.
2.)...

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 mean family income for a random sample of 600 suburban
households in Loganville shows that a 95 percent confidence
interval is ($43,100, $59,710). Alma is conducting a test of the
null hypothesis H0: µ = 42,000 against the alternative hypothesis
Ha: µ ≠ 42,000 at the α = 0.05 level of significance. Does Alma
have enough information to conduct a test of the null hypothesis
against the alternative?
A No, because the value of σ is not known
B...

1. The P-value of a test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is false, that
the test statistic will take a value at least as extreme as that
actually observed.
d. the probability, assuming the null hypothesis is true, that
the test statistic will take a value at least as extreme as that
actually observed.
2. The P-value...

For each of the following statements, identify whether the
statement is true or false, and explain why. Please limit each
response to no more than 3 sentences.
i) A p-value is the probability that the null hypothesis is
false. ii) A chi-square test statistic can never be negative.
iii) If we reject the null hypothesis that a population
proportion is equal to a specific value, then that specific value
will not be contained in the associated confidence interval.
iv) If...

True/False, if false briefly explain.
1. The margin of error for a confidence interval used for an
opinion poll does not take into account the fact that people who
did not answer the poll questions may have had different responses
from those who did answer the questions.
2. If the p-value for a significance test is 0.35, we can
conclude that the null hypothesis has a 35% chance of being
true.
3. A student project used a confidence interval to...

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...

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...

A 95% CI for true average amount of warpage (mm) of laminate
sheets under specified conditions was calculated as (6.81, 6.95),
based on a sample size of n = 17 and the assumption that amount of
warpage is normally distributed. (a) Suppose you want to test H0: μ
= 7 versus Ha: μ ≠ 7 using α = 0.05. What conclusion would be
appropriate, and why? Since the null value of 7 is in the 95%
confidence interval we reject...

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 _____....

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