Question

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let
*x*_{1} be a random variable that represents the
score of a mother on an empathy test (as regards her baby). Let
*x*_{2}be the empathy score of a father. A random
sample of 37 mothers gave a sample mean of *x*_{1} =
67.00. Another random sample of 27 fathers gave
*x*_{2} = 61.04. Assume that *σ*_{1}
= 10.92 and *σ*_{2} = 11.62.

(a) Let *μ*_{1} be the population mean of
*x*_{1} and let *μ*_{2} be the
population mean of *x*_{2}. Find a 95% confidence
interval for *μ*_{1} – *μ*_{2}. (Use
2 decimal places.)

lower limit | |

upper limit |

(b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 95% confidence level?

Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score.

Answer #1

Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.

option A

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let
x1 be a random variable that represents the
score of a mother on an empathy test (as regards her baby). Let
x2 be the empathy score of a father. A random
sample of 31 mothers gave a sample mean of x1 =
69.55. Another random sample of 36 fathers gave
x2 = 59.00. Assume that σ1
= 10.71 and σ2 =...

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let x1
be a random variable that represents the score of a mother on an
empathy test (as regards her baby). Let x2 be the empathy score of
a father. A random sample of 29 mothers gave a sample mean of x1 =
67.68. Another random sample of 34 fathers gave x2 = 60.36. Assume
that σ1 = 10.85 and σ2 =...

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let
x1 be a random variable that represents the
score of a mother on an empathy test (as regards her baby). Let
x2 be the empathy score of a father. A random
sample of 27 mothers gave a sample mean of x1 =
69.21. Another random sample of 25 fathers gave
x2 = 60.53. Assume that σ1
= 11.97 and σ2 =...

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let
x1 be a random variable that represents the
score of a mother on an empathy test (as regards her baby). Let
x2 be the empathy score of a father. A random
sample of 27 mothers gave a sample mean of x1 =
67.00. Another random sample of 26 fathers gave
x2 = 59.85. Assume that σ1
= 11.90 and σ2 =...

A study of parental empathy for sensitivity cues and baby
temperament (higher scores mean more empathy) was performed. Let
x1 be a random variable that represents the
score of a mother on an empathy test (as regards her baby). Let
x2 be the empathy score of a father. A random
sample of 27 mothers gave a sample mean of x1 =
69.89. Another random sample of 40 fathers gave
x2 = 61.55. Assume that ?1
= 12.04 and ?2 =...

1. The following data represent petal lengths (in cm) for
independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica:
x1; n1 = 35
5.1
5.9
6.1
6.1
5.1
5.5
5.3
5.5
6.9
5.0
4.9
6.0
4.8
6.1
5.6
5.1
5.6
4.8
5.4
5.1
5.1
5.9
5.2
5.7
5.4
4.5
6.4
5.3
5.5
6.7
5.7
4.9
4.8
5.9
5.1
Petal length (in cm) of Iris setosa:
x2; n2 = 38
1.5
1.9
1.4
1.5
1.5...

The U.S. Geological Survey compiled historical data about Old
Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let
x1 be a random variable that represents the
time interval (in minutes) between Old Faithful eruptions for the
years 1948 to 1952. Based on 8800 observations, the sample mean
interval was x1 = 61.2 minutes. Let
x2 be a random variable that represents the
time interval in minutes between Old Faithful eruptions for the
years 1983 to 1987. Based on 24,404...

The U.S. Geological Survey compiled historical data about Old
Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let
x1 be a random variable that represents the
time interval (in minutes) between Old Faithful eruptions for the
years 1948 to 1952. Based on 9200 observations, the sample mean
interval was x1 = 63.8 minutes. Let
x2 be a random variable that represents the
time interval in minutes between Old Faithful eruptions for the
years 1983 to 1987. Based on 24,872...

How profitable are different sectors of the stock market? One
way to answer such a question is to examine profit as a percentage
of stockholder equity. A random sample of 35 retail stocks such as
Toys 'R' Us, Best Buy, and Gap was studied for
x1, profit as a percentage of stockholder
equity. The result was x1 = 15.0. A random
sample of 38 utility (gas and electric) stocks such as Boston
Edison, Wisconsin Energy, and Texas Utilities was studied...

The U.S. Geological Survey compiled historical data about Old
Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let
x1 be a random variable that represents the
time interval (in minutes) between Old Faithful eruptions for the
years 1948 to 1952. Based on 9800 observations, the sample mean
interval was x1 = 64.4 minutes. Let
x2 be a random variable that represents the
time interval in minutes between Old Faithful eruptions for the
years 1983 to 1987. Based on 24,404...

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