Question

Suppose we are interested in testing the null hypothesis that the mean of a normal distribution is 25 lbs vs. the alternative hypothesis that it is less than 25 lbs using α = 0.1.  

We take a sample of size 11 and find the sample mean to be 23.4 and the sample standard deviation to be 5.72.

What would be the rejection region for this test?

Reject if

a) | t 0 | ≥ 1.81

b) t 0 ≥ 1.81

c) t 0 ≤ − 1.81

d) | t 0 | ≥ 1.80

e)t 0 ≥ 1.80

f) t 0 ≤ − 1.80

g) | t 0 | ≥ 1.37

h) t 0 ≥ 1.37

i) t 0 ≤ − 1.37

j) | t 0 | ≥ 1.36

k) t 0 ≥ 1.36

l)

Answer 1

rejection region for this test : i) to ≤−1.37

below are test details:

null hypothesis: HO: μ		=	25
Alternate Hypothesis: Ha: μ		<	25
0.1 level with left tail test and n-1= 10 df, critical t=				-1.37
Decision rule :reject Ho if test statistic t<-1.37
	population mean μ=	25
	sample mean 'x̄=	23.400
	sample size   n=	11.00
	sample std deviation s=	5.720
	std error 'sx=s/√n=	1.725
	test stat t ='(x-μ)*√n/sx=	-0.928

since test statistic is not in rejection region we can not reject null hypothesis