decision rules & z values?

sylverhawk · #1 $Old$ July 3rd, 2009, 12:14 AM

i am lost on this one..anyone help please?

Hypothesis test results:
μ : mean of Variable
H0 : μ = 98.6
HA : μ ≠ 98.6
Std. Dev. not specified

Variable

n

Sample Mean

Std. Err.

Z-Stat

P-value

temp

130

98.24923

0.06430442

-5.4548235

<0.0001

Write a decision rule using the critical z-value as the criteria as to whether or not you will reject the null hypothesis.
Write a conclusion that states what the results of your hypothesis test have shown in terms of mean body temperature for adults

sylverhawk · #2 $Old$ July 3rd, 2009, 12:22 AM

that should say:
variable: temp
n: 130
sample mean:98.24923
std.err : 0.06430442
z-stat: -5.4548235
p-value : <0.0001

matheagle · #3 $Old$ July 4th, 2009, 12:30 AM

This is a two sided test, where you are going to accept HAH.

The test stat is ${\overline X-\mu_0\over s/\sqrt n}={98.24923-98.6\over .06430442}=-5.4548235$

NOW the p-value is either $2P(t_{129}>5.4548235)\approx 0$ if you are assuming normality
or via the Central Limit Theorem $2P(Z>5.4548235)\approx 0$ , but since a t approaches a Z as n goes to infinity these two are close.

BUT the point here is that your p-value is small, since your test stat is large (in a negative sense),
so we will reject HO and laugh our way to HA.
Your temperature is not normal, nor is Mr Fantasy normal.