# hypothesis test for mean less than number

• Apr 6th 2011, 07:33 AM
Caption12
hypothesis test for mean less than number
a sample of 16 egg is take froom normal disribution. variance is unknown
sample mean xbar is 4.49 and sample st dev, s, is 1.231
you wish to do a test if the population mean is less than 5

state h0 and h1, calculate test statistic and use the t disribution to find what level you can accept or reject h0.

now i think the h0 is populationmean=5, h1 not equal 5?

test statistic, t=(xbar-5)/(s/root of n)
which i make =-1.657 please tell me if this right because if its wrong my lookup table will not even help..

so now what i do with the t disribution table because i am confuse. i know degree of freedom is n-1 = 15. but i am confuse.
• Apr 6th 2011, 03:37 PM
TKHunny
1) If you are using H1: Mean <> 5, you have a 2-tailed test. That MAY be what you want and it may be the most appropriate place to start.
2) You WILL need to select a level of significance. Remember to divide by 2 for a 2-tailed test.
• Apr 6th 2011, 04:01 PM
pickslides
Quote:

Originally Posted by Caption12
you wish to do a test if the population mean is less than 5

$\displaystyle H_0: \mu \geq 5$

$\displaystyle H_1: \mu <5$
• Apr 6th 2011, 10:31 PM
Caption12
so it means is 1-tail

my answer for t is negative but the t value table is positive

t distribution is symmetric about zero. If T is a random variable which follows t-distribution, then $\displaystyle P(T<-t_{observed})=P(T>t_{observed})$; so you can get the probability from a positive t-table.