3. SAT coaching: A sample of 32 students took a class designed to improve their SAT math scores. Following are their scores before and after the class. Before After Before After 383 420 394 430 334 368 513 525 378 396 483 482 467 488 447 482 470 489 440 479 473 473 439 451 443 448 435 431 459 473 451 454 426 428 453 463 493 525 491 511 382 382 526 529 473 474 473 493 408 407 440 466 433 434 481 482 478 490 459 455 502 508 399 404 Can you conclude that the mean increase in score is less than 15 points? State a conclusion. Use the α = 0.05 level of significance.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
3. SAT coaching: A sample of 32 students took a class designed to improve their SAT math scores. Following are their scores before and after the class.
|
Before |
After |
Before |
After |
|---|---|---|---|
|
383 |
420 |
394 |
430 |
|
334 |
368 |
513 |
525 |
|
378 |
396 |
483 |
482 |
|
467 |
488 |
447 |
482 |
|
470 |
489 |
440 |
479 |
|
473 |
473 |
439 |
451 |
|
443 |
448 |
435 |
431 |
|
459 |
473 |
451 |
454 |
|
426 |
428 |
453 |
463 |
|
493 |
525 |
491 |
511 |
|
382 |
382 |
526 |
529 |
|
473 |
474 |
473 |
493 |
|
408 |
407 |
440 |
466 |
|
433 |
434 |
481 |
482 |
|
478 |
490 |
459 |
455 |
|
502 |
508 |
399 |
404 |
Can you conclude that the
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