Question

2. Two ride-sharing companies, A and B, provide service for a
certain city. A random sample of 52 trips made by Company A and a
random sample of 52 trips made by Company B were selected, and the
number of miles traveled for each trip was recorded. The difference
between the sample means for the two companies

(A−B) was used to construct the 95 percent confidence interval
(1.86,2.15).

Which of the following is a correct interpretation of the
interval?

A. We are 95 percent confident that the difference in sample
means for miles traveled by the two companies is between 1.86 miles
and 2.15 miles.

B. We are 95 percent confident that the difference in
population means for miles traveled by the two companies is between
1.86 miles and 2.15 miles.

C. The probability is 0.95 that the difference in sample means
for miles traveled by the two companies is between 1.86 miles and
2.15 miles.

D. The probability is 0.95 that the difference in population
means for miles traveled by the two companies is between 1.86 miles
and 2.15 miles.

E. About 95 percent of the differences in miles traveled by
the two companies are between 1.86 miles and 2.15 miles.

3. Two community service groups, J and K, each have less than
100 members. Members of both groups volunteer each month to
participate in a community-wide recycling day. A study was
conducted to investigate whether the mean number of days per year
of participation was different for the two groups. A random sample
of 45 members of group J and a random sample of 32 members of group
K were selected. The number of recycling days each selected member
participated in for the past 12 months was recorded, and the means
for both groups were calculated. A two-sample t-test for a
difference in means will be conducted. Which of the following
conditions for inference have been met?

I. The data were collected using a random method.

II. Each sample size is less than 10 percent of the population
size.

III.
Eachsamplesizeislargeenoughtoassumenormalityofthesampling

distribution of the difference in sample means.

A. I only

B. II only

C. III only

D. I and III only E. I, II, and III

Answer #1

Solution

**Q 2**

First of all, confidence interval is a means of predicting or estimating the population parameter and not sample statistic. Sample statistic is used to arrive the confidence interval. Further, as the very name suggests, the confidence level represents how confident one can be about the interval estimate.

Hence **Option B Answer 1**

**Q 3**

Two-sample t-test is valid only if the Normality condition and the randomness of data are satisfied. But, even when the distribution of the base data is not known, tests involving means can be done with t-test if the sample size(s) are large enough, say 30 or more. In that case, by Central Limit Theorem, sample average follows Normal distribution.

Hence **Option D Answer 2**

**DONE**

The following results are for independent random samples taken
from two populations.
Sample 1
Sample 2
n1 = 40
n2 = 50
x1 = 32.2
x2 = 30.1
s1 = 2.6
s2 = 4.3
(a) What is the point estimate of the difference between the two
population means?
(b) What is the degrees of freedom for the t
distribution?
(c) At 95% confidence, what is the margin of error?
(d) What is the 95% confidence interval for the difference
between...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.8
55.6
39.1
43.2
25.0
37.7
32.2
41.4
10.5
27.1
29.5
32.1
38.6
39.5
15.6
36.3
42.4
20.2
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

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

The following results are for independent random samples taken
from two populations.
Sample 1
Sample 2
n1 = 20
n2 = 30
x1 = 22.8
x2 = 20.1
s1 = 2.6
s2 = 4.6
(a)
What is the point estimate of the difference between the two
population means? (Use
x1 − x2.
)
(b)
What is the degrees of freedom for the t distribution?
(Round your answer down to the nearest integer.)
(c)
At 95% confidence, what is the margin...

The following results are for independent random samples taken
from two populations.
Sample 1
Sample 2
n1 = 20
n2 = 30
x1 = 22.5
x2 = 20.1
s1 = 2.2
s2 = 4.6
(a)
What is the point estimate of the difference between the two
population means? (Use
x1 − x2.
)
(b)
What is the degrees of freedom for the t distribution?
(Round your answer down to the nearest integer.)
(c)
At 95% confidence, what is the margin...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.4
55.3
38.7
43.7
24.7
37.7
32.6
41.3
10.7
27.5
29.8
32.8
38.1
39.1
15.5
36.7
42.1
20.8
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

Independent random samples were selected from two quantitative
populations, with sample sizes, means, and standard deviations
given below. n1 = n2 = 80, x1 = 125.3, x2 = 123.6, s1 = 5.7, s2 =
6.7
Construct a 95% confidence interval for the difference in the
population means (μ1 − μ2). (Round your answers to two decimal
places.)
Find a point estimate for the difference in the population
means.
Calculate the margin of error. (Round your answer to two decimal
places.)

The following results are for independent random samples taken
from two populations.
Sample 1
Sample 2
n1 = 20
n2 = 30
x1 = 22.5
x2 = 20.1
s1 = 2.9
s2 = 4.6
a) What is the point estimate of the difference between the two
population means? (Use
x1 − x2.)
b) What is the degrees of freedom for the t
distribution? (Round your answer down to the nearest integer.)
c) At 95% confidence, what is the margin of...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.7
55.8
38.9
43.3
25.3
37.7
32.9
41.7
10.7
27.4
29.2
32.6
38.3
39.6
15.2
36.8
42.5
20.1
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

A random sample of companies in electric utilities (I),
financial services (II), and food processing (III) gave the
following information regarding annual profits per employee (units
in thousands of dollars).
I
II
III
49.3
55.7
38.7
43.3
25.0
37.3
32.6
41.5
10.9
27.1
29.4
32.9
38.5
39.9
15.5
36.5
42.2
20.4
Shall we reject or not reject the claim that there is no
difference in population mean annual profits per employee in each
of the three types of companies? Use...

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