A student wants to see if the number of times a book has been checked out of the tibrary 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 tibrary 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 28 375 390 13 277 321 27 342 30 299 33 272 32 401 33 295 32 417 27 400 41 402 The correlation coefficient: (round to 3 decimal places) The equation y-a-bx is: (round to 3 decimal places) The hypotheses are: Họ:p-0 (ne tinear relationship) HAip40 inear relationship) iclaim) Since a is 0.05 the critical value is 2.179 and 2.179 (round to 3 decimal places) The test value ]round to 3 decimal places) The pvalue is: The decision is to O reject H, O do net reject H, 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 encugh evidence to reject the claim that there is a linear relationship. O There is enough evidence to support the claim that there is a tinear relationship. O There is not encugh 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 tibrary 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 tibrary 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 28 375 390 13 277 321 27 342 30 299 33 272 32 401 33 295 32 417 27 400 41 402 The correlation coefficient: (round to 3 decimal places) The equation y-a-bx is: (round to 3 decimal places) The hypotheses are: Họ:p-0 (ne tinear relationship) HAip40 inear relationship) iclaim) Since a is 0.05 the critical value is 2.179 and 2.179 (round to 3 decimal places) The test value ]round to 3 decimal places) The pvalue is: The decision is to O reject H, O do net reject H, 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 encugh evidence to reject the claim that there is a linear relationship. O There is enough evidence to support the claim that there is a tinear relationship. O There is not encugh evidence to support the claim that there is a linear relationship.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.2: Box-and-whisker Plots
Problem 1E
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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:The image is a worksheet related to testing the correlation between the number of times a book has been checked out of a library and the number of pages in the book. Below is a detailed transcription suitable for an educational website:
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**Research Question:**
A student wants to investigate if the number of times a book has been checked out in the past year and the number of pages in the book are related. She hypothesizes that the number of times a book has been checked out is a predictor of the number of pages it has. She has randomly sampled 14 books from the library, testing her claim at a 0.05 level of significance.
**Data Table:**
| Number of times checked out | Number of pages |
|-----------------------------|-----------------|
| 12 | 311 |
| 20 | 348 |
| 28 | 379 |
| 19 | 370 |
| 31 | 321 |
| 30 | 342 |
| 33 | 299 |
| 36 | 270 |
| 31 | 327 |
| 35 | 497 |
| 27 | 410 |
| 31 | 379 |
| 32 | 417 |
| 41 | 402 |
**Statistical Analysis:**
1. **Correlation Coefficient:**
\( r = \underline{\quad} \) (round to 3 decimal places)
2. **Linear Regression Equation:**
The equation \( y = a + bx \):
- \( a = \underline{\quad} \) (round to 3 decimal places)
- \( b = \underline{\quad} \) (round to 3 decimal places)
3. **Hypotheses:**
- Null hypothesis (\( H_0 \)): \( \rho = 0 \) (no linear relationship)
- Alternative hypothesis (\( H_a \)): \( \rho \neq 0 \) (linear relationship)
4. **Critical Values:**
Since \( \alpha = 0.05 \), the critical values are \(\pm 2.179\).
5. **Test Value \( t \):**
\( t = \underline{\quad} \) (round to 3 decimal places)
6. **P-value:**
P-value = \
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