Question

True or False?

A) You do a hypothesis test on 2 means, if you reject H0 at the significance level of 10%, then you will reject H0 at the significance level of 5%. T or F?

B) If the variances of 2 normal populations are unknown but assumed to be unequal, the appropriate statistic to compare the 2 means is the t of student (we assume here a small sample) . T or F?

C) If the variances of 2 normal populations are unknown but assumed to be equal, the appropriate statistic to compare the 2 means is the t of student (we assume here a small sample). T or F?

Answer #1

A) if we have test to test means and we reject the null hypothesis Ho at the significance level 10% , then we may be or may not be reject the null hypothesis Ho at 5% significance level . Depends on value of test statistic .

So answer is False .

B) If we have to test two population means and variances of 2 normal populations are unknown but assumed to be unequal

Also sample size is small

Then the appropriate test is student t test .

So answer is True

C) If we have to test two population means and variances of 2 populations are unknown but assumed to be equal. Sample size is small.

Then appropriate test is student t test

So answer is True.

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...

1) Consider a test of
H0 : μ = μ0
vs.
H0 : μ <
μ0.
Suppose this test is based on a sample of size 8, that
σ2 is known, and that the underlying population
is normal. If a 5% significance level is desired, what would be the
rejection rule for this test?
Reject H0 if zobs <
-1.645
Reject H0 if tobs <
-1.894
Reject H0 if zobs <
-1.960
Reject H0 if tobs <
-2.306
2)
Which...

11 . Choosing the appropriate test statistic
You are interested in the difference between two population means.
Both populations are normally distributed, and the population
variances σ212 and σ222 are known. You use an independent samples
experiment to provide the data for your study. What is the
appropriate test statistic?
F = √[2/n1 + 2/n2]
F = s1/s2
z = (x̄1 – x̄2) / √[σ2/n1 + σ2/n2]
z = (p̂1 – p̂2) / √[p̂(1 – p̂)(1/n1 + 1/n2)]
Suppose instead...

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...

Consider the following hypothesis test.
H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
The following results are from independent samples taken from
two populations assuming the variances are unequal.
Sample 1
Sample 2
n1 = 35
n2 = 40
x1 = 13.6
x2 = 10.1
s1 = 5.7
s2 = 8.2
(a) What is the value of the test statistic? (Use x1
− x2. Round your answer to three decimal
places.)
(b) What is the degrees of...

Hypothesis Test for the Difference in Population Means
(σσ Unknown)
You wish to test the following claim (HaHa) at a significance
level of α=0.005α=0.005.
Ho:μ1=μ2Ho:μ1=μ2
Ha:μ1>μ2Ha:μ1>μ2
You believe both populations are normally distributed, but you do
not know the standard deviations for either. Let's assume that the
variances of the two populations are not equal. You obtain the
following two samples of data.
Sample #1
60
62.8
60.2
48.5
61.8
52.7
65.1
66.3
71.4
72.2
63.8
59.5
70.5
58.3
79.6
57.4...

Suppose you are going to test the hypothesis that two
populations have the same mean. You find sample averages of 6 and
7.5 and sample 1 has a standard deviation of 16 and sample 2 has a
standard deviation of 15 and both samples have 32 observations. In
this case the test statistic follows the t distribution with 61
degrees of freedom. True or False: you reject the null hypothesis
at the .01 level of significance. true or false

T F 1. A p-value of .008 in hypothesis testing means there is
only a .8% chance we could get such sample statistics from the
population if the null hypothesis is as stated. Such an event is
considered unlikely and we would reject the null hypothesis.
T F 2. As a general rule in hypothesis testing, it is always
safer to set up your alternate hypothesis with a greater-than or
less-than orientation.
_____3. If the level of significance is .02...

The following is sample information. Test the hypothesis that
the treatment means are equal. Use the 0.02 significance level.
Treatment 1
Treatment 2
Treatment 3
7
2
5
8
3
7
6
5
10
7
3
6
a. State the null hypothesis and the alternate
hypothesis.
H0:
(The treatment
means are not all the same or The treatment means are the
same?)
H1:
(The treatment
means are not all the same or The treatment means are...

State which hypothesis test would be appropriate under the
following conditions. We know that our two data sets come from
approximately normally distributed populations and that they have
very different variances.
The Answer Options are:
2-sample t-test with unequal variances
2-sample t-test with equal variances
t-test Mann-Whitney
U Test
z-test

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