What is the test statistic? Explain. ( I am having trouble with finding both the p-value & test statistic) What is the p-value? Explain.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
For each of the 32 National Football League teams, the numbers of points scored and allowed during the 2018 season are shown below.
|
Team |
Wins | Points Scored | Points Allowed | Team | Wins | Points Scored |
Points Allowed | |
| New York Jets | 4 | 333 | 441 | Chicago Bears | 12 | 421 | 283 | |
| Cleveland Browns | 7 | 359 | 392 | Philadelphia Eagles | 9 | 367 | 348 | |
| Denver Broncos | 6 | 329 | 349 | Tennessee Titans | 9 | 310 | 303 | |
| Jacksonville Jaguars | 5 | 245 | 316 | Kansas City Chiefs | 12 | 565 | 421 | |
| Minnesota Vikings | 8 | 360 | 341 | Baltimore Ravens | 10 | 389 | 287 | |
| Oakland Raiders | 4 | 290 | 467 | Houston Texans | 11 | 402 | 316 | |
| Cincinnati Bengals | 6 | 368 | 455 | Buffalo Bills | 6 | 269 | 374 | |
| Washington Redskins | 7 | 281 | 359 | New Orleans Saints | 13 | 504 | 353 | |
| Los Angeles Rams | 13 | 527 | 384 | Detroit Lions | 6 | 324 | 360 | |
| Tampa Bay Buccaneers | 5 | 396 | 464 | Seattle Seahawks | 10 | 428 | 347 | |
| Miami Dolphins | 7 | 319 | 433 | Indianapolis Colts | 10 | 433 | 344 | |
| Pittsburgh Steelers | 9 | 428 | 360 | San Francisco 49ers | 4 | 342 | 435 | |
| Green Bay Packers | 6 | 376 | 400 | Dallas Cowboys | 10 | 339 | 324 | |
| New England Patriots | 11 | 436 | 325 | Carolina Panthers | 7 | 376 | 382 | |
| New York Giants | 5 | 369 | 412 | Los Angeles Chargers | 12 | 428 | 329 | |
| Arizona Cardinals | 3 | 225 | 425 | Atlanta Falcons | 7 | 414 | 423 | |
The linear relationship between points allowed and points scored is very weak.
Null & Hypothesis: H0: ρ ≥ 0 and H1: ρ < 0
- What is the test statistic? Explain. ( I am having trouble with finding both the p-value & test statistic)
- What is the p-value? Explain.
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