Question

a. For the following degrees of freedom, list the critical values for a one-tailed and two-tailed test at a .01 and .05 level of significance.

.01 .05

df = (Infinity) ___ ___ (One-tailed test)

df = (Infinity) ___ ___ (Two-tailed test)

b. Refer to Table 8.4 in Chapter 8. How do the critical values you listed in the previous question compare with those listed for the z-distribution. Explain.

Answer #1

Solution

a) The critical values for One-tailed and Two-tailed test at 0.01 & 0.05 level of significance for degrees of freedom at infinity is given below

**One tailed test**

At 0.01 level of significance df = infinity the critical value is 2.326

At 0.05 level of significance df = infinity the critical value is 1.645

**Two tailed test**

At 0.01 level of significance df = infinity the critical value is 2.576

At 0.05 level of significance df = infinity the critical value is 1.960

b) For the z- distribution

taking the above critical values as z value

1.645=0.9495 = lower limit of right 5% tail

1.96=0.9750 = lower limit of right 2.5% tail

2.32=0.9898 = lower limit of right 1% tail

2.57=0.9949 = lower limit of right 0.5% tail

Find the critical value of t from Appendix D for the following
situations. Specify the correct degrees of freedom, whether the
value is “+/-“ or is “+ or –“ and, if the actual df value isn’t the
table, specify which you used.
a) N = 31, α = .05, one-tailed one sample
t-test _______________________________
b) N = 25, α = .01, two-tailed one sample t-test
_______________________________
c) N = 26, α = .05, one-tailed one sample
t-test _______________________________
d) N...

1. Calculate the critical degrees of freedom and
identify the critical t value for a single-sample t test in each of
the following situations, using p=.05 for all scenarios. Then,
state whether the null hypothesis would fail to be rejected or
rejected:
a. Two-tailed test, N = 14, t = 2.05, (df=
Answer:, critical t = Answer:, Reject or Fail to Reject
Ho:
Answer:
b. One-tailed test, N = 14, t = 2.05, (df=
Answer:, critical t = Answer:, Reject...

Determine (a) the χ2 test statistic, (b) the degrees
offreedom, (c) the critical value using alpha equals α=0.05,
and(d) test the hypothesis at the alpha equals α=0.05 level of
significance.
Outcome
A
B
C
D
Observed
48
52
51
49
Expected
50
50
50
50
Ho : Pa = Pb = Pc = Pd = 1/4
H1 : At least one proportions is different from the others.
a) The test statistic is
b) The degrees of freedom are one less...

State the total degrees of freedom for the following
t-tests. (If you need to use ∞, enter INFINITY.)
(a)n = 21
for a one-independent sample t-test
(b)df1 = 12,
n2 = 25
for a two-independent sample t-test
(c) critical value = 1.645 for a one-tailed test,
α = 0.05
(d) critical value = 63.657 for a two-tailed test,
α = 0.01

Assume the computed t-statistic was t0=1.987
Find the t-critical value for a one-tailed test at the 0.05
significance level with 19
degrees of freedom. Is there sufficient evidence to reject the
null hypothesis?
Find the t-critical value for a one-tailed test at the 0.05
significance level with a sample
size of 30. Is there sufficient evidence to reject the null
hypothesis?
Find the t-critical value for a two-tailed test at the 0.05
significance level with 15
degrees of freedom. Is...

Using the t
distribution table, identify the t statistics that would
set the critical regions in a hypothesis test for the following
alphas and n’s (2 points each). Remember to check
direction and df when choosing the
column/row.
One-tailed test, α =
.05, n = 10
Two-tailed test, α =
.05, n = 10
One-tailed test, α =
.01, n = 15
Two-tailed test, α =
.01, n = 20

R language
Exercise 1. Here, we look at how t critical values behave as
their df (degrees of freedom) increases:
a. First, what is z.05?
b. Second, if you look at t.05,20, t.05,40, t.05,60, . . . (t
values for α = .05 with df = 20, 40, 60, continuing up by 20 each
time)
i. for what df is the value of t.05,df first different from z.05
by less than .05?
ii. for what df is the value of...

Complete parts (a) through (c) below.
(a) Determine the critical value(s) for a right-tailed test
of a population mean at the alphaα=.10 with 15 degrees of freedom.
tcrit=
b) Determine the critical value(s) for a left-tailed test of a
population mean at the α=0.05 level of significance based on a
sample size of n=20
c) Determine the critical value(s) for a two-tailed test of a
population mean at the α=.01 level of significance based on a
sample size of n=18

Use the given information to find the number of degrees of
freedom, the critical values
chi Subscript Upper L Superscript 2χ2L
and
chi Subscript Upper R Superscript 2χ2R,
and the confidence interval estimate of
sigmaσ.
It is reasonable to assume that a simple random sample has been
selected from a population with a normal distribution.Nicotine in
menthol cigarettes
8080%
confidence;
nequals=2929,
sequals=0.250.25
mg.
LOADING...
Click the icon to view the table of Chi-Square critical
values.
df=
(Type a whole number.)

A researcher conducts two t tests. Test 1 is a one-tailed test
with a smaller sample size at a .05 level of significance. Test 2
is a one-tailed test with a larger sample size at a .05 level of
significance. What do you know about the critical values for each
test?

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