Question

A bakery is considering buying one of two gas ovens. The bakery requires that the temperature remain constant during a baking operation. A study was conducted to measure the variance in temperature of the ovens during the baking process. The variance in temperature before the thermostat restarted the flame for the Monarch oven was 2.4 for 22 measurements. The variance for the Kraft oven was 3.5 for 10 measurements. Does this information provide sufficient reason to conclude that there is a difference in the variances for the two ovens? Assume measurements are normally distributed and use a 0.02 level of significance.

(a) Find F. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is significant evidence to show a difference in variances. Reject the null hypothesis, there is not significant evidence to show a difference in variances.     Fail to reject the null hypothesis, there is not significant evidence to show a difference in variances. Fail to reject the null hypothesis, there is significant evidence to show a difference in variances.

Answer 1

a)

Ho     σ21	=	σ22
Ha : σ22	≠	σ22

	n1    =	10
	n2    =	22
df of numerator v1 =n1-1=		9
df of denominator v2=n2-1 =		21
s12 =	3.5
s22 =	2.4

Test statistic =s12/s22 =

1.46 (try 0.69 if this comes wrong and reply)

ii)

from excel: p value =fdist(1.46,9,21)*2 =0.4528

b)

Fail to reject the null hypothesis, there is not significant evidence to show a difference in variances.