Question

An ethnographer at Tulane University in New Orleans is interested in vampyric graffiti. He believes that the Twilight Movies and novels have caused an increase in vampire-related graffiti in his city. In 1972, an ethnographer collected an exhaustive catalog of all the graffitis in New Orleans, and from these he estimates that the average level of vampyric graffitis is 2.01 per parish, with a standard deviation of 4.10. He samples 6 parishes in the city and collects data on the number of graffitis that refer to vampires. He finds an average of 4.25 vampyric graffitis per parish today. Demonstrate that he has not found evidence for a significant increase in vampyric graffiti. What statistical power does this test have? What would the power be if he increased his sample size to 12, and assumed the same mean difference between the groups? Based on that power, should he do a second study with a larger sample size? Use an alpha level of

0.05.

Answer 1

TS = (Xbar - mu)/(sd/sqrt(n))

= (4.25 - 2.01)/(4.1/sqrt(6))

= 1.33825

since TS < 1.645 (critical value at 0.05 level one-sided)

the result is not significant

power = reject the null hypothesis whenthe null is false

we reject when Xbar >

> 2.01 + 1.645 * 4.10/sqrt(6)

> 4.76343

For actual

P(Xbar > 4.76343)

= P(Z > ( 4.76343 - )/(4.10/sqrt(6))

you have not given , hence I can't calculate the power

if sample size is increased, then power increases