## Related questions with answers

Sharks. Great white sharks are big and hungry. Here are the lengths in feet of 44 great whites:

Length | 18.7 | 12.3 | 18.6 | 16.4 | 15.7 | 18.3 | 14.6 | 15.8 | 14.9 | 17.6 | 12.1 |
---|---|---|---|---|---|---|---|---|---|---|---|

Length | 16.4 | 16.7 | 17.8 | 16.2 | 12.6 | 17.8 | 13.8 | 12.2 | 15.2 | 14.7 | 12.4 |

Length | 13.2 | 15.8 | 14.3 | 16.6 | 9.4 | 18.2 | 13.2 | 13.6 | 15.3 | 16.1 | 13.5 |

Length | 19.1 | 16.2 | 22.8 | 16.8 | 13.6 | 13.2 | 15.7 | 19.7 | 18.7 | 13.2 | 16.8 |

(a) Examine these data for shape, center, spread, and outliers. The distribution is reasonably Normal except for one outlier in each direction. Because these are not extreme and preserve the symmetry of the distribution, use of the t procedures is safe with 44 observations.

(b) Give a 95% confidence interval for the mean length of great white sharks. Based on this interval, is there significant evidence at the 5% level to reject the claim "Great white sharks average 20 feet in length"?

(c) Before accepting the conclusions of (b), you need more information about the data. What would you like to know?

Solution

Verified(a) Create a histogram. The width of the bars has to be the same and the height has to be equal to the frequency.

Shape: Roughly symmetric/bell-shaped and thus the distribution is roughly normal.

Center: $\overline{x}=15.5864$

Spread: $s=2.5499$

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