MS 150 quiz 11 • Name:

17 April 2009

A study of the length in centimeters of Cephalopholis argus [English: Peacock hind or blue-spotted grouper, Kosraen: Kalsrik, Mortlockese: Sawei, Mwoakillese: Widir, Pohnpeian: Mwoalusulus, Woleaian: Hali] found in the markets on Pohnpei from January to May 2006 was done by Kevin Rhodes, M. Tupper, Scotty Malakai, Don Jack, Clement Wichilmel, Richard Ben, and Kirino and Anson Olpet. The data is based loosely on this work. For the purposes of this quiz, consider that the average length for a population of blue-spotted groupers which has not been overharvested is μ = 30 centimeters. In other words, the population mean μ is 30 centimeters for a healthy Cephalopholis argus grouper population. Run a hypothesis test to determine whether or not the Cephalopholis argus grouper population found in Pohnpeian markets has a population mean μ of 30 centimeters.

1. __________ Calculate the sample size n.
2. __________ Calculate the minimum.
3. __________ Calculate the maximum.
4. __________ Calculate the range.
5. __________ Calculate the midrange.
6. __________ Calculate the mode.
7. __________ Calculate the median.
8. __________ Calculate the sample mean x.
9. __________ Calculate the sample standard deviation sx.
10. __________ Calculate the sample coefficient of variation CV.
11. __________ Calculate the standard error for the mean SE.
12. __________ What is the point estimate for the population mean μ based on the sample mean x?
13. Write out the null hypothesis that the population mean μ is 30 centimeters: H₀:
14. Write out the alternate hypothesis: H₁:
    
    Run a hypothesis test at a risk of a type I error α = 0.05
15. ____________________ Calculate the value of t_critical
16. ____________________ Calculate the value of the t-statistic t
17. _________________________________ Do we reject or fail to reject the null hypothesis?
18. ____________________ Is the sample mean x statistically significantly different from the population mean μ of 30 cm for a an unharvested, healthy Cephalopholis argus grouper population?
19. ____________________ Calculate the p-value.
20. ____________________ Calculate the maximum confidence interval for which the difference in length is statistically significant.

Hypothesis Testing
Statistic or Parameter	Symbol	Equations	OpenOffice
Relationship between confidence level c and alpha α for two-tailed tests		1 − c = α
Calculate t-critical for a two-tailed test	tc		=TINV(α;df)
Calculate a t-statistic t	t		=(x - μ)/(sx/SQRT(n))
Calculate a two-tailed p-value from a t-statistic	p-value		= TDIST(ABS(t);df;2)