Question

1. Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume the population standard deviations are equal.

Suppose you are interested if a name brand candle is made from the same wax as the generic store brand candle. You decide that they smell the same, so the only question left is if they last as long as a generic brand candle (of the same size, type). These two brands of candles are tested and the average time they burned (in hours) are recorded. The summary statistics are given below:

  

Name Brand	Generic Store Brand
n=35	n=40
19.4 hours	15.1hours
s=1.4 hours	s=0.8 hours

Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean (indicating that there is no difference in the population means). Perform a complete hypothesis test, including a diagram of the critical values.

Answer 1