H0 always has an "=" sign, never "<", ""≤", ">", "≥" or "≠". Only
"H1" has those. So b), c), e), and f) are immediately eliminated. That leaves
only a) and d). It can't be a) because GPA is not a probability and p stands for
probability. So the only choice left is d).
That's the way to get it by elimination. But we could tell the answer without
using elimination because we are testing the mean 2.9, so it's H0:μ=2.9.
Also we are testing to see if μ is DIFFERENT from 2.9, not whether it is GREATER
or LESS than 2.9. "DIFFERENT FROM means" "not equal to", "≠", because it could be
different from 2.9 it were either GREATER or LESS than 2.9.
The test is:
two-tailed because it's "≠",
Based on a sample of 60 people, the sample mean GPA was 2.9 with a standard deviation of 0.05
The p-value is:_______________(to 2 decimals)
On your TI-84, press STAT
Highlight TESTS
Choose Z-Test
Z-Test
Inpt:Data Stats <---Highlight Stats
μo:2.9
σ:0.05
x̄:2.9
n:60
μ:≠μo <μo >μo <--Highlight the first
Calculate <--Highlight this
press enter
μ≠2.9
z=0
p=0.999999999
x̄=2.9
n=60
The p-value is 0.999999999 which rounds to 1.00 to 2 decimals
Based on this we fail to reject the null hypothesis, because p is greater than
0.01.
Remember the poem:
"If p is high, the null will fly."
"If p is low, the null must go."
If it "will fly", we fail to reject it.
If it "must go", we reject it.
In this case, p is "high" because it is more than the significance level 0.01
Edwin
