Question

At the .01 level of significance, test whether the claim is correct that the variance in the annual temperature in the United States (excluding Hawaii and Alaska) is 3.5 degrees Fahrenheit. A sample of the last 101 years in Michigan produced an average annual temperature 44.4 F with a variance of 3.8 F. What does the decision imply?

a)The variance in the annual temperature is greater than 3.5 degrees.

b)The variance in the annual temperature is less than 3.5 degrees.

c)The variance in the annual temperature is 3.5 degrees.

d)The variance in the annual temperature is not 3.5 degrees.

Answer 1

null hypothesis:     Ho:				σ2 =	3.5
Alternate hypothesis: Ha:				σ2 ≠	3.5

for sample size n:				=	101
s2				=	3.8000

for 99 % CI and given df critical values of F      =			67.3276		&	140.1695
Decision rule:reject Ho if test statistic X2 in critical region:			67.3276		< X2 >	140.1695

test stat :

=χ2=(n-1)s2/σ2=

108.57

as test statistic does not fall in rejection region:

c)The variance in the annual temperature is 3.5 degrees.