A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 14 books from the library, test her claim at a 0.05 level of significance. number of times checked out number of pages 27 371 12 348 28 375 9 390 13 277 321 27 342 30 299 33 272 32 401 33 295 32 417 27 400 41 402 The correlation coefficient: r- (round to 3 decimal places) The equation y=a+bx is: (round to 3 decimal places) y= The hypotheses are: Ho:p = 0 (no linear relationship) HA:P + 0 (linear relationship) (claim) Since a is 0.05 the critical value is -2.179 and 2.179 The test value is: (round to 3 decimal places) The p-value is: (round to 3 decimal places) The decision is to O reject Ho O do not reject Ho Thus the final conclusion sentence is O There is enough evidence to reject the claim that there is a linear relationship. O There is not enough evidence to reject the claim that there is a linear relationship. O There is enough evidence to support the claim that there is a linear relationship. O There is not enough evidence to support the claim that there is a linear relationship.
A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 14 books from the library, test her claim at a 0.05 level of significance. number of times checked out number of pages 27 371 12 348 28 375 9 390 13 277 321 27 342 30 299 33 272 32 401 33 295 32 417 27 400 41 402 The correlation coefficient: r- (round to 3 decimal places) The equation y=a+bx is: (round to 3 decimal places) y= The hypotheses are: Ho:p = 0 (no linear relationship) HA:P + 0 (linear relationship) (claim) Since a is 0.05 the critical value is -2.179 and 2.179 The test value is: (round to 3 decimal places) The p-value is: (round to 3 decimal places) The decision is to O reject Ho O do not reject Ho Thus the final conclusion sentence is O There is enough evidence to reject the claim that there is a linear relationship. O There is not enough evidence to reject the claim that there is a linear relationship. O There is enough evidence to support the claim that there is a linear relationship. O There is not enough evidence to support the claim that there is a linear relationship.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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Transcribed Image Text:A student wants to investigate whether the number of times a book has been checked out from the library in the past year is related to the number of pages it has. She hypothesizes that the frequency of checkouts can predict the number of pages. The student randomly sampled 14 books from the library to test her hypothesis at a 0.05 level of significance.
**Data Sample:**
| number of times checked out | number of pages |
|-----------------------------|-----------------|
| 27 | 371 |
| 12 | 348 |
| 28 | 375 |
| 9 | 390 |
| 13 | 277 |
| 1 | 321 |
| 27 | 342 |
| 30 | 299 |
| 33 | 272 |
| 32 | 401 |
| 33 | 295 |
| 32 | 417 |
| 27 | 400 |
| 41 | 402 |
**Statistical Analysis:**
1. **Correlation Coefficient (r):** Enter the calculated value, rounded to three decimal places.
2. **Equation of the Line (y = a + bx):** Find and round the values of 'a' and 'b' to three decimal places.
3. **Hypotheses:**
- Null Hypothesis \( H_0 \): \(\rho = 0\) (no linear relationship)
- Alternative Hypothesis \( H_A \): \(\rho \neq 0\) (there is a linear relationship)
4. **Critical Values:** With \(\alpha = 0.05\), the critical values are -2.179 and 2.179.
5. **Test Value:** Compute and round to three decimal places.
6. **P-value:** Round the calculated p-value to three decimal places.
**Decision Making:**
- Decide whether to reject or not reject \( H_0 \) based on the test results.
**Conclusion Options:**
- There is enough evidence to reject the claim that there is a linear relationship.
- There is not enough evidence to reject the claim that there is a linear relationship.
- There is enough evidence to support the claim that there is a linear relationship.
- There is not enough evidence to support the claim that there is a linear relationship.
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