List 3 measures one
can take to increase the power of an experiment. Explain
why your measures result in greater power.

Population 1 mean = 36

Population 2 mean = 45

Both population standard deviations are 10.

Sample size (per group) 16.

What is the probability that a t test will find a significant
difference between means at the 0.05 level? Give results
for both one- and two-tailed tests. Hint: the power of
a one-tailed test at 0.05 level is the power of
a two-tailed
test at 0.10.

Rank order the following in terms of power. n is the sample size per group.

Population 1 Mean

n

Population 2 Mean

Standard Deviation

a

29

20

43

12

b

34

15

40

6

c

105

24

50

27

d

170

2

120

10

Alan, while snooping around his grandmother's basement stumbled
upon a shiny object protruding from under a stack of boxes
. When he reached for the object a genie miraculously materialized
and stated: "You have found my magic coin. If you flip
this coin an infinite number of times you will notice that
heads will show 60% of the time." Soon after the genie's
declaration he vanished, never to be seen again. Alan, excited
about his new magical discovery, approached his friend Ken
and told him about what he had found. Ken was skeptical of
his friend's story, however, he told Alan to flip the coin
100 times and to record how many flips resulted with heads.

(a) What is the probability that Alan will be able convince
Ken that his coin has special powers by finding a p value
below 0.05 (one tailed).
Use the Binomial
Calculator (and some trial and error)

(b) If Ken told Alan to flip the coin only 20 times,
what is the probability that Alan will not be able to convince
Ken (by failing to reject the null hypothesis at the 0.05
level)?