Question

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.

Answer #1

**Solution:- C. Both (ii) and (iii) are true.**

(i) The variances in both populations of variable X are assumed to be zero. False

(ii) Samples should be independently and randomly selected from the populations. True

(iii) Both samples have the same variance. True

For a confidence interval to be valid, numbers of assumptions are made as follows:

1) The two population we samples are normal.

2) The two population have the same variances.

3) The two samples are random samples from the population of interest.

4) The two samples are independent.

**Hence from the above assumptions 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 (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.

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...

Indicate whether the following statement is true or false.
1. When estimating a confidence interval for the difference
between the means of two independent populations, the pooled
variance is the average of two sample variances, if the two sample
sizes are equal.
2. Both the t-distribution and standard normal distribution have
the same mean, but the t-distribution has a smaller standard
deviation than the standard normal distribution.
3. The standard deviation of the distribution
of (i.e. standard error of the mean)...

Describe a confidence interval for the difference in means
between two population by stating
1. a pair of populations composed of the same type of individuals
and a quantitative variable on those populations,
2. sizes and degrees of freedom of samples from those
populations,
3. the means of those samples, and
4. the standard deviations of those samples. Then state
5. a confidence level and find
6. find the interval. Finally, perform a test of significance
concerning the difference in...

Consider the following statements.
(i) The samples must be independent.
(ii) The population variances must be equal.
(iii) The populations must follow an
F-distribution.
Determine if each of the following is an assumption of analysis of
variance (1) or is not an assumption of analysis
of variance (2)?

Consider the following statements concerning confidence interval
estimates:
A. The use of the pooled variance estimator when constructing a
confidence interval for the difference between means requires the
assumption that the population variances are equal.
B. The width of a confidence interval estimate for the proportion,
or for mean when the population standard deviation is known, is
inversely proportional to the square root of the sample size.
C. To determine the sample size required to achieve a desired
precision in...

Confidence Interval for 2-Means (2 Sample T-Interval)
Given two independent random samples with the following
results:
n1=11
n2=17
x1¯=118
x2¯=155
s1=18
s2=13
Use this data to find the 99% confidence interval for the true
difference between the population means. Assume that the population
variances are equal and that the two populations are normally
distributed. Round values to 2 decimal places.
Lower and Upper endpoint?

Independent random samples were selected from populations 1 and
2. The sample sizes, means, and variances are as follows.
Population
1
2
Sample Size
30
64
Sample Mean
11.4
6.9
Sample Variance
1.37
4.15
(a) Find a 95% confidence interval for estimating the difference
in the population means (μ1 −
μ2). (Round your answers to two decimal
places.)
to

1- Which of the following statements is true?
I. For a certain confidence level, you get a higher margin of
error if you reduce your sample size.
II. For a given sample size, increasing the margin of error will
mean higher confidence.
III. For a fixed margin of error, smaller samples will mean
lower confidence.
I only
II only
III only
II and III only
All of them
----------------------------------
2- Which must be true about a 90% confidence interval based...

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