Question

The p-value is greater than the significance level.

(a) We can have a Type I error

(b) The absolute value of the test statistic is less than the absolute value of the t critical value

(c) If we had used a larger value for alpha the p-value would have been smaller

(d) We must have had a two tail test

Answer #1

(b) The absolute value of the test statistic is less than the absolute value of the t critical value.

We know the decision rule in terms of p-value and critical value are given as below:

We reject the null hypothesis when the p-value is less than the alpha value or level of significance and we do not reject the null hypothesis when the p-value is greater than the alpha value.

We reject the null hypothesis when the absolute test statistic value is greater than the absolute critical value, and we do not reject the null hypothesis when the absolute test statistic value less than the critical value.

We have a one sample test for the population mean. The
significance level is a fixed value. Suppose we increase the sample
size. Assume the true mean equals the null mean.
(a) The t critical value moves closer to zero.
(b) The size of the rejection region decreases
(c) The probability of a Type I error decreases
(d) The probability of a Type I error increases

Multiple Choice Questions
Q1. In a hypothesis test, Beta is best described
by
P (Type I error)
P (Test Stat>|Observed Stat|)
Power
P (Type II error)
Q2. Which alternative hypothesis would I need
to double the p-value in a test for the mean?
No feasible answer
Lower tailed alternative
Two sided alternative
Upper tailed alternative
Suppose our p-value is .184. What will our conclusion be
at alpha levels of .10, .05, and .01?
We will reject Ho at alpha=.10 or...

For the given significance test, explain the meaning of a Type I
error, a Type II error, or a correct decision as specified. A
health insurer has determined that the "reasonable and customary"
fee for a certain medical procedure is $1200. They suspect that the
average fee charged by one particular clinic for this procedure is
higher than $1200. The insurer performs a significance test to
determine whether their suspicion is correct using α = 0.05. The
hypotheses are:
H0:...

1. Which of the following statements is correct?
a.
For a given level of significance, the critical value of
Student's t increases as n increases.
b.
A test statistic of t = 2.131 with d.f. = 15 leads to a
clear-cut decision in a two-tailed test at d = .05.
c.
It is harder to reject the null hypothesis when conducting a
two-tailed test rather than a one-tailed test.
d.
If we desire α = 0.10 then a p-value of...

Statistical significance (alpha level;
p-value) reflects the odds that
a particular finding could have
occurred by chance.
If the
p-value for a difference between
two groups is 0.05, it would be expected to occur by chance just 5
times out of 100 (thus, it is likely to be a “real” difference). We
define a p-value of less than 0.05 to indicate statistical
significance.
Suppose a pizza place claims their delivery times are 30 minutes
or less on average but you...

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...

1. You have a two-tailed test. The t critical value is 2.36 and
the test statistic is 3.11. Assume the null hypothesis is true. The
result is (a) Type I error (b) Type II error (c) Correct
decision
2. You have a right-tailed test. The t critical value is 1.74
and the test statistic is 1.46. Assume the null hypothesis is true.
The result is (a)Type I error (b) Type II error (c) Correct
decision
3. You have a right-tailed...

Provide a real world example of a Type I error.
2. Explain what a critical value is, and explain how
it is used to test a hypothesis.
3. Explain what a p-value is, and explain how it is
used to test a hypothesis.
4. How do we decide whether to use a z test or a t
test when testing a hypothesis about a population mean?

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.

Assume that the significance level is alpha equals 0.05. Use the
given information to find the? P-value and the critical? value(s).
The test statistic of z = -1.07 is obtained when testing the claim
that p greater than 0.4.

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