MS 150 Statistics q10 • Name:

The discovery of Pluto by careful telescopic observation in 1930 added a ninth planet to the solar system. Then in 1978 better technology revealed that what was seen in 1930 was not a single planet, but two smaller objects orbiting each other. The larger object retained the name Pluto, the smaller object was name Charon. This discovery meant that Pluto was significantly smaller than any other planet, and was actually smaller than some moons of other planets.

Beginning in 2000 further improvements in astronomical technologies led to the discovery of many more Pluto and Charon sized objects beyond Pluto. By 2005 eleven other objects were discovered in orbits beyond Pluto, an area of the solar system called the Kuiper belt. A debate broke out among astronomers. Should astronomy add eleven more planets to the official list of planets? The Kuiper belt contains thousands of small objects thought to be composed primarily of ices of water, nitrogen, methane, along with rocky minerals such as silicates, olivines, and pyroxenes. How big is big enough to be a planet? If the eleven new Kuiper belt objects were not planets, then neither was Pluto. Ultimately astronomers decided to refer to Pluto and the other Kuiper belt objects as planetoids, not planets. Thus the solar system has only eight planets starting with Mercury near the sun and ending with Neptune as the outermost planet.

1. __________ What is the level of measurement?
2. __________ Find the sample size n.
3. __________ Find the minimum.
4. __________ Find the maximum.
5. __________ Find the range.
6. __________ Find the midrange.
7. __________ Find the mode.
8. __________ Find the median.
9. __________ Find the sample mean x.
10. __________ Find the sample standard deviation sx.
11. __________ Find the sample coefficient of variation CV.
12. __________ Find the z-score for Pluto.
13. ____________________ Is the z-score for Pluto ordinary or unusual?
14. ____________________ Calculate the standard error of the mean SE.
15. ____________________ Find the degrees of freedom n − 1.
16. ____________________ Calculate t-critical t_c using an alpha α = 0.05
17. ____________________ Find the margin of error for the mean E.
18. Calculate the 95% confidence interval for the population mean μ
    
    p(__________ ≤ μ ≤__________) = 0.95
19. Based on the z-score and the confidence interval, should Pluto be restored to "planet" status or remain in its new "planetoid" category? Support your answer with your z-score and confidence interval results.