Question

**8. Confidence intervals for estimating the difference in
population means**

Elissa Epel, a professor of health psychology at the University of California–San Francisco, studied women in high- and low-stress situations. She found that women with higher cortisol responses to stress ate significantly more sweet food and consumed more calories on the stress day compared with those with low cortisol responses, and compared with themselves on lower stress days. Increases in negative mood in response to the stressors were also significantly related to greater food consumption. These results suggest that psychophysiological responses to stress may influence subsequent eating behavior. Over time, these alterations could impact both weight and health.

You are interested in studying whether college juniors or college sophomores consume more calories. You ask a sample of n₁ = 35 college juniors and n₂ = 40 college sophomores to record their daily caloric intake for a week.

The average daily caloric intake for college juniors was M₁ = 2,423 calories, with a standard deviation of s₁ = 237. The average daily caloric intake for college sophomores was M₂ = 2,679 calories, with a standard deviation of s₂ = 256.

To develop a confidence interval for the population mean difference μ₁ – μ₂, you need to calculate the estimated standard error of the difference of sample means, s(M1 – M2)(M1 – M2). The estimated standard error is s(M1 – M2)(M1 – M2) =57.25 .

Use the Distributions tool to develop a 95% confidence interval for the difference in the mean daily caloric intake of college juniors and college sophomores.

0123Standard Normalt Distribution

Select a Distribution

The 95% confidence interval is256 to .

This means that you are % confident that the unknown difference between the mean daily caloric intake of the population of college juniors and the population of college sophomores is located within this interval.

Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is to .

This means that you are % confident that the unknown difference between the mean daily caloric intake of the population of college juniors and the population of college sophomores is located within this interval.

The new confidence interval is than the original one, because the new level of confidence is than the original one.

Answer #1

Calculate the 95% confidence interval for the difference
(mu1-mu2) of two population means given the following sampling
results. Population 1: sample size = 18, sample mean = 26.66,
sample standard deviation = 1.04. Population 2: sample size = 15,
sample mean = 10.79, sample standard deviation = 1.71.

Calculate the 99% confidence interval for the difference
(mu1-mu2) of two population means given the following sampling
results. Population 1: sample size = 12, sample mean = 20.36,
sample standard deviation = 0.57. Population 2: sample size = 7,
sample mean = 16.32, sample standard deviation = 0.85.

Calculate the 99% confidence interval for the difference
(mu1-mu2) of two population means given the following sampling
results. Population 1: sample size = 9, sample mean = 14.42, sample
standard deviation = 0.47. Population 2: sample size = 14, sample
mean = 10.78, sample standard deviation = 1.69.

Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
include negative and positive numbers.
No. Increasing the confidence level leads to...

Suppose you calculate a 95% confidence interval for the
difference in population means. The confidence interval contains
both negative and positive values.
Will a 99% confidence interval based on the same data contain
both negative and positive numbers as well? Choose the correct
response from the options provided below.
A. Yes. Keeping all other values the same, increasing the
confidence level leads to a wider interval which would still
include negative and positive numbers.
B.
No. Increasing the confidence level...

Recall the method used to obtain a confidence interval for the
difference between two population means for matched samples.
(a) The following data are from matched samples taken from two
populations. Compute the difference value for each element. (Use
Population 1 − Population 2.)
Element
Population
Difference
1
2
1
11
8
2
7
8
3
9
6
4
12
7
5
13
10
6
15
15
7
15
14
(b) Compute d.
(c) Compute the standard
deviation sd. (Round
your answer...

Why is it important to compute confidence intervals for
estimates of population means or percentages?
A. Because every sample statistic is subject to error.
B. Because managers don’t like point estimates.
C. Because every sample statistic must be presented without
error.
D. Because the sample statistic = the population parameter.
The calculated z or t value is inversely related to the size of
the differences between two means or percentages (i.e., as the
difference between two means or percentage increases,...

You want to calculate a 95% confidence interval (CI) for the
difference between the means of two variables. The variables are
from populations with normal distributions and those distributions
have the same standard deviation (σ). To make your estimate you
will take the same number of samples from each population,
calculate the mean for each sample, calculate the difference
between those sample means, and then add or subtract the term that
defines the CI. If you want the width of...

Construct the indicated confidence interval for the difference
between the two population means. Assume that the two samples are
independent simple random samples selected from normally
distributed populations. Do not assume that the population standard
deviations are equal.
Two types of flares are tested and their burning times are
recorded. The summary statistics are given below.
Brand X
Brand Y
n = 35
n = 35
x-bar = 19.4 min
x-bar = 15.1 min
s = 1.4 min
s =...

The MINITAB printout shows a test for the difference in
two population means.
Two-Sample
T-Test and CI: Sample 1, Sample 2
Two-sample T for Sample
1 vs Sample 2
N
Mean
StDev
SE Mean
Sample 1
5
29.00
3.00
1.3
Sample 2
7
28.89
3.63
1.4
Difference = mu (Sample
1) - mu (Sample 2)
Estimate for
difference: 0.11
95% CI for difference:
(-4.3, 4.5)
T-Test of difference =
0 (vs not =):
T-Value = 0.06 P-Value
= 0.96...

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