Question


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.

Homework Answers

Answer #1

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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