B) two brands of firelog (duraheat and everflame) are tested to see which on burns longer. a sample of 22 duraheat logs burns for an average of 192 minutes with a standard deviation of 12 minutes. A sample of 28 everflame logs burns for an average of 206 minutes with standard deviation of 18 minutes. Test whether the logs have a different average burn time at alpha= .01
C) Calculate a 99%confidence interval for the difference in average burn time from part b) above. Interpret the interval.
Let's denote the data for duraheat burns by subscript 1 and for everflame by 2.
Data given for group 1:
Sample mean, m1 = 192
Sample SD, S1 = 12
Sample size, n1 = 22
Data given for group 2:
Sample mean, m2 = 206
Sample SD, S2 = 18
Sample size, n2 = 28
The hypotheses are:
H0: 1 = 2
Ha: 12
Calculating standard error:
SE = (S12/n1 + S22/n2)0.5 = (122/22 + 182/28)0.5 = 4.256
Calculating test statistic:
t = (m2-m1)/SE = (206-192)/4.256 = 3.29
Degrees of freedom, df = n1+n2-2 = 48
The corresponding p-value for this t-score is:
p = 0.0018
Since the p-value is smaller than the significance level of = 0.01, so we have to reject the null hypothesis.
Thus, the logs have significantly different average burn time.
Hope this helps !
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