Question

Using the data below, determine if there is evidence to conclude that the variance of weekly prices during 2009 is less than 10% at 5% significance level.

Date Gasoline Price

Jan 03, 2000$1.26

Jan 10, 2000$1.25

Jan 17, 2000$1.27

Jan 24, 2000$1.31

Jan 31, 2000$1.31

Feb 07, 2000$1.32

Feb 14, 2000$1.35

Feb 21, 2000$1.40

Feb 28, 2000$1.41

Mar 06, 2000$1.49

Mar 13, 2000$1.51

Mar 20, 2000$1.51

Mar 27, 2000$1.48

Apr 03, 2000$1.48

Apr 10, 2000$1.45

Apr 17, 2000$1.42

Apr 24, 2000$1.41

May 01, 2000$1.39

May 08, 2000$1.43

May 15, 2000$1.47

May 22, 2000$1.49

May 29, 2000$1.51

Jun 05, 2000$1.54

Jun 12, 2000$1.61

Jun 19, 2000$1.66

(The data is much longer that this, so if you could just show me the formulas on excel so I can do it on my own, I would appreciate that much more.)

Thanks

Answer 1

using excel we have

Chi-Square Test of Variance
			Formula used
Data
Null Hypothesis                        s^2=	0.1
Level of Significance	0.05
Sample Size	25		COUNT(A2:A26)
Sample Standard Deviation	0.105748		STDEV.S(A2:A26)
Intermediate Calculations
Degrees of Freedom	24		C6-1
Half Area	0.025		C5/2
Chi-Square Statistic	2.6838		C10*C7^2/C4
Lower-Tail Test
Lower Critical Value	13.8484		CHISQ.INV.RT(1-C5, C10)
p-Value	0.0000		1-CHISQ.DIST.RT(C12, C10)
Reject the null hypothesis

since p value is 0.0000 which is less than 0.05 so we conclude that the variance of weekly prices during 2000 is less than 10%