5. Is it better to fish from the shore or a boat? Let x be a random variable representing the number of hours taken to catch a fish. The table below contains the data taken over several months for B from the shore, and A from a boat. Oct Nov Dec Jan Feb Mar Apr B (shore) A (boat) 1.6 1.8 2.0 3.2 3.9 3.6 3.3 1.5 1.4 1.6 2.2 3.3 3.0 3.8 Use a 1% level of significance to determine if there is a difference in the population mean hours per fish using a boat compared with fishing from shore. (This is a paired difference problem.)
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.
#5 It must be in the format of the second picture.
![**Sample and Population Analysis for Statistical Testing**
**Random Variable:** \(\bar{X}\)
**Special Considerations/Characteristics:**
(Blank)
**Given:**
\[ P\left(\bar{X} \leq 6820\right) = 0.0030 \]
**Question:**
(Blank)
**Sample Information:**
- \( n = 50 \)
- \(\bar{x} = 6820\)
**Population Information:**
- \(\mu = 7500\)
- \(\sigma = 1750\)
**Sampling Distribution:**
**Type:** Normal
**Why Justified:** Central Limit Theorem (CLT), as \(n > 30\)
**Test Statistic:** \(Z\)
**Calculations:**
1. **Mean of Sampling Distribution:**
\[ \mu_{\bar{X}} = \mu = 7500 \]
2. **Standard Error:**
\[ \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{1750}{\sqrt{50}} \approx 247.4874 \]
3. **Test Statistic Value:**
\[ Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}} = \frac{6820 - 7500}{247.4874} = -2.75 \]
**Diagram Explanation:**
There is a bell curve representing a normal distribution, centered at the population mean, 7500. The area to the left of the point \(-2.75\) is shaded, indicating the probability \(P(Z \leq -2.75) = 0.0030\). This area corresponds to the lower tail of the distribution, which is significant at this level.
**Conclusion:**
The probability that the sample mean \(\bar{X}\) is less than or equal to 6820 is very small (0.3%), suggesting that such an observation is unusual if the true population mean is indeed 7500. This outcome may be considered statistically significant depending on the chosen threshold for significance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff59662fb-eaec-4b3d-a1b9-c848915bfa7b%2Ff5a22481-de03-4148-bb84-b0f77cef36be%2Fkcefwz_processed.jpeg&w=3840&q=75)
![### Statistical Analysis of Fishing and Health Data
#### Fishing Time Analysis
**Problem 5: Fishing from Shore vs. Boat**
Is it better to fish from the shore or a boat? Let \( x \) be a random variable representing the number of hours taken to catch a fish. The table below contains the data taken over several months for \( B \) from the shore, and \( A \) from a boat.
| Month | B (shore) | A (boat) |
|-------|-----------|----------|
| Oct | 1.6 | 1.5 |
| Nov | 1.8 | 1.4 |
| Dec | 2.0 | 1.6 |
| Jan | 3.2 | 2.2 |
| Feb | 3.9 | 3.3 |
| Mar | 3.6 | 3.0 |
| Apr | 3.3 | 3.8 |
Use a 1% level of significance to determine if there is a difference in the population mean hours per fish using a boat compared with fishing from the shore. (This is a paired difference problem.)
#### Hay Fever Rate Analysis
**Problem 6: Age Groups and Hay Fever Rates**
In a location, two random samples were taken concerning the rate of hay fever per 1000 population.
- **Sample 1** (\( n_1 = 14 \)) contained people under 25.
- **Sample 2** (\( n_2 = 16 \)) contained people over 50.
\[
\bar{X}_1 = 109.5, \quad s_1 = 15.41 \\
\bar{X}_2 = 99.36, \quad s_2 = 11.57 \\
\]
Assume that the hay fever rate in each group has an approximately normal distribution. Do the data indicate that the over 50 group has a significantly lower hay fever rate? (Use \( \alpha = 5\% \))
(Note: Several of these problems have been adapted from our text.)
#### Testing Framework
- **Random Variable:** ______________
- **Special considerations/characteristics:** ______________
- **Given:**
- **Question:**
- **B. What Type:**
- **Why Justified](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff59662fb-eaec-4b3d-a1b9-c848915bfa7b%2Ff5a22481-de03-4148-bb84-b0f77cef36be%2Fswivbbm.jpeg&w=3840&q=75)
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