c) What was the sample mean of the number of hours spent relaxing or pursuing enjoyable activities on an average workday? Give your answer to two decimal places. hours
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
C.
![**Transcription for Educational Website**
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The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey collected responses from 1,154 US residents. The survey is conducted face-to-face with an in-person interview of a randomly-selected sample of adults. One of the questions on the survey is:
"After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?"
A 95% confidence interval from the 2010 GSS survey is 3.53 to 3.83 hours.
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**Questions and Solutions:**
a) Which of the following is a valid interpretation of this confidence interval?
- [ ] 95% of Americans relax or pursue enjoyable activities between 3.53 and 3.83 hours on an average workday.
- [x] Using the methods of this survey will result in an interval that captures the true population mean 95% of the time.
- [ ] 95% of Americans in this sample relax or pursue enjoyable activities between 3.53 and 3.83 hours on an average workday.
**Solution:** The correct interpretation of the confidence interval is: "Using the methods of this survey will result in an interval that captures the true population mean 95% of the time."
b) Suppose the researchers think a 90% confidence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval? Assume the standard deviation has remained constant since 2010.
- [ ] Larger
- [x] Smaller
**Solution:** A 90% confidence interval would be smaller than the 95% confidence interval.
c) What was the sample mean of the number of hours spent relaxing or pursuing enjoyable activities on an average workday? Give your answer to two decimal places.
**Answer:** __3.68__ hours
**Explanation:**
- The confidence interval provides a range of values (3.53 to 3.83 hours) that captures the true population mean with 95% confidence. The sample mean is typically located at the center of this interval. Therefore, the sample mean is calculated as follows:
\[ \text{Sample Mean} = \frac{3.53 + 3.83}{2} = 3.68 \]
Thus, the sample](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7856584-59fd-4634-ab45-c4c5f6444c59%2F7ec94910-2695-4d78-b8f0-d24bb586f874%2Fp0fez1m_processed.png&w=3840&q=75)
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