Question

a. We are testing H_{0}: μ_{1} - μ_{2} =
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) H_{0}
and conclude that the group 1 population average is _____(smaller/
larger) than the group 2 population average.

It is possible that we could be making a _____ (Type I /Type II
error).

b. We are testing H_{0}: μ = 15. Our t statistic is
1.53.

We can tell that in our sample, the sample average was _____(greater/ less than )15.

We should expect the 95% confidence interval to _______ (include /exclude) 15.

We should expect the p-value to be ______( less than .05 /greater than .05 /equal to .05)

We should _______( reject /fail to reject )H_{0}.

It is possible that we could be making a _____(Type I /Type II) error.

Answer #1

a.

We are testing H_{0}: μ_{1} - μ_{2} = 0.
Our 95% confidence interval is (-23.95,-7.41).

We should expect the t-statistic to be **less than
-2**

We should expect the p-value to be **less than
.05**.

We should **reject** H_{0} and conclude
that the group 1 population average is **smaller**
than the group 2 population average.

It is possible that we could be making a **Type
I.**

b.

We are testing H_{0}: μ = 15. Our t statistic is
1.53.

We can tell that in our sample, the sample average was
**greater than** 15.

We should expect the 95% confidence interval to
**include** 15.

We should expect the p-value to be **greater than
.05.**

We should **fail to reject** H_{0}.

It is possible that we could be making a **Type
II** error**.**

H0: μ1 - μ2 = 0
x1 = 81849, x2 = 88021
standard error of x1 - x2 = 1430
The approximate 95% CI for μ1 - μ2
is to (_____, ______)
The result of the hypothesis test is:
a)Reject H0, because the null value is inside the 95%
CI.
b)Reject H0, because the null value is outside the
95% CI.
c)Fail to reject H0, because the null value is inside
the 95% CI.
d)Fail to reject H0, because the null...

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

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...

We are testing the hypothesis
H0:p=.75
Ha:p<.75
for the # the proportion of people who find an enrollment
website “easy to use.” The test will be based on a simple random
sample of size 400 and at a 1% level of significance. Recall that
the sample proportion vary with mean p and standard deviation
= sqroot( p(1-p)/n)
You shall reject the null hypothesis if
The P_value of the test is less than 0.01
a) Find the probability of a type...

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...

Ho p(greater than and equal to) .15
H p( less than) .15
z= -1.176
p value =.1190 > .05
so we fail to reject our null hypothesis.
95% confidence interaval = .1387 (plus minus) .01886015
between 12% and 15.76%
when would the consortium make a type 1 error? When would the
consortium make a type II error? In addition to a narrative
explanation of these types of errors, also create a table to help
in the understanding of these types...

For the following hypothesis test, where H0:
μ ≤ 10; vs. HA: μ > 10, we reject
H0 at level of significance α and conclude that
the true mean is greater than 10, when the true mean is really 14.
Based on this information, we can state that we have:
Made a Type I error.
Made a Type II error.
Made a correct decision.
Increased the power of the test.

Question 3 This question concerns some concepts about
hypothesis testing and confidence interval. For each part below,
you must explain your answer.
(a) Suppose we are doing a one-sample t test at the 5% level of
significance where the hypotheses are H0 : µ = 0 vs H1 : µ > 0.
The number of observations is 8. What is the critical value? [2
marks]
(b) Suppose we are doing a hypothesis test and we can reject H0
at the...

1. Which statement is incorrect?
A. The null hypothesis contains the equality sign
B. When a false null hypothesis is not rejected, a Type II error
has occurred
C. If the null hypothesis is rejected, it is concluded that the
alternative hypothesis is true
D. If we reject the null hypothesis, we cannot commit Type I
error
2. When carrying out a large sample test of H0: μ ≤ 10
vs. Ha: μ > 10 by using a critical value...

Consider the following competing hypotheses: Use Table 2.
H0: μD ≥ 0;
HA: μD < 0
d-bar = −2.3, sD = 7.5, n =
23
The following results are obtained using matched samples from
two normally distributed populations:
a.
At the 10% significance level, find the critical value(s).
(Negative value should be indicated by a minus sign. Round
intermediate calculations to 4 decimal places and final answer to 2
decimal places.)
Critical value
b.
Calculate the value of the...

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