e. Select a value of a, the probability of Type l error. Interpret this value in thé words of O A. There would still be sufficient evidence to reject the null hypothesis if a>0.202. B. There would still be sufficient evidence to reject the null hypothesis if a = 0.001 O C. There would still be sufficient evidence to reject the null hypothesis if a>0.001 D. There would still be suficient evidence to reject the null hypothesis if a<0.202.
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.
![**Trap Spacing Measurements Analysis for Red Spiny Lobster Fishermen**
*Introduction:*
Trap spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are provided in the accompanying table. Let \(\mu\) represent the average of the trap spacing measurements for the population of red spiny lobster fishermen. The mean (\(\bar{x}\)) and the standard deviation (s) of the sample measurements are \(\bar{x} = 88.4\) meters and \(s = 12.2\) meters, respectively. Suppose you want to determine if the true value of \(\mu\) differs from 95 meters. Complete parts a through h below.
| 91 | 97 | 105 | 94 | 80 | 68 | 84 |
**Part b:**
Since \(\bar{x} = 88.4\) is less than 95, a fisherman wants to reject the null hypothesis. What are the problems with using such a decision rule?
- **A.** To reject the null hypothesis, the problem must specify the critical value of t.
- **B.** To reject the null hypothesis, the problem must specify the value of \(\alpha\) and the probability that the test will lead to rejection and then consult the t or z table depending on the size of the sample.
- **C.** To reject the null hypothesis, the problem must specify the critical value of z.
- **D.** To reject the null hypothesis, the problem must specify the sample size.
**Part c: Compute the value of the test statistic.**
\[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} = \frac{88.4 - 95}{12.2/\sqrt{7}} = -\frac{6.6}{4.6188} = -1.42 \]
(Round to two decimal places as needed.)
**Part d: Find the approximate p-value of the test.**
Using a t-distribution table or statistical software, you find:
\[ \text{p-value} = 0.205 \]
(Round to three decimal places as needed.)
**Part e: Select the value of \(\alpha\), the probability of Type I error. Interpret this value in the words of the problem.**
- **A.** There would still be sufficient evidence to reject the null hypothesis if](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05cf7d90-82b1-4600-90af-c1fd169002d7%2F9708939e-51b5-42f3-8e5e-57bd34450523%2Fbd2o13k_processed.jpeg&w=3840&q=75)
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