Question

26. Consider the following statements.

(i). If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

(ii). If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.

(iii). The critical value of t for a two-tail test of the difference of two means, a level of significance of 0.10 and sample sizes of seven and fifteen, is ±1.734.

Answer #1

**Answer:**

1) **True**

The basic assumption when calculation for difference between two population means is that one population is independent of the sampe. Else the test is not possible

2) **False**

We never assume that the populations are normal and have equal variances when testing difference between population means

3) **False**

The critical values are +- 1.725 and not +- 1.734

Consider the following statements. When estimating a confidence
interval for the difference between the means of two independent
populations.
(i) The variances in both populations of variable X are assumed to
be zero.
(ii) Samples should be independently and randomly selected from
the populations.
(iii) Both samples have the same variance.
A.
Only (ii) is true.
B.
Only (i) is true.
C.
Both (i) and (iii) are true.
D.
Both (ii) and (iii) are true.

Consider the following statements. When estimating a confidence
interval for the difference between the means of two independent
populations.
(i) The variances in both populations of variable X are assumed to
be zero.
(ii) Samples should be independently and randomly selected from
the populations.
(iii) Both samples have the same variance.
A.
Only (i) is true.
B.
Only (ii) is true.
C.
Both (ii) and (iii) are true.
D.
Both (i) and (iii) are true.

Consider the following statements. When estimating a confidence
interval for the difference between the means of two independent
populations. (i) The variances in both populations of variable X
are assumed to be zero. (ii) Samples should be independently and
randomly selected from the populations. (iii) Both samples have the
same variance. A. Only (ii) is true. B. Only (i) is true. C. Both
(ii) and (iii) are true. D. Both (i) and (iii) are true.

In testing the difference between two population means when
population standard deviations are
unknown, there are many cases depending upon whether the two
population standard deviations
are equal or not. Therefore, before testing the difference
between two population means, the
equality of two population variances must be tested first. Let
the sample data from population #1
be? =10,?̅ =97.4,? =8.8769andfrompopulation#2be? =7,?̅ =110,?
=30.2214. 111 222
Answer the following five questions assuming the level of
significance=0.1.
23. In testing the hypothesis...

In testing the difference between two population means using two
independent samples, the population standard deviations are assumed
to be unknown, each sample size is 30, and the calculated test
statistic z = 2.56. If the test is a two-tailed and the 5% level of
significance has been specified, the conclusion should be:
a.
none of these answers is correct.
b.
choose two other independent samples.
c.
reject the null hypothesis.
d.
not to reject the null hypothesis.

Which of the following is not an assumption underlying the
independent-measures t formula for hypothesis testing?
The observations within each sample must be independent.
The two populations from which the samples are selected must be
normal.
The two samples must have equal sample sizes.
The two populations from which the samples are selected must
have equal variances.

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...

Shea wants to estimate the difference between two population
means and plans to use data collected from two independent simple
random samples of sizes ?1=27 and ?2=32. She does not know the
population standard deviations, so she plans to construct a
two-sample ?-confidence interval for the difference in the two
means.
Use a ?‑distribution table to determine the positive ?‑critical
value needed to construct a 95% confidence interval using a
conservative estimate of the number of degrees of freedom.
Enter...

What is the main difference between one population and two
populations hypothesis testing?

Construct a 90% confidence interval estimate for the difference
between two population means given the following sample data
selected from two normally distributed populations with equal
variances:
Sample 1 Sample 2
29
25 31
42 39
38
35
35 37
42 40
43
21
29
34
46 39
35

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