Given the information in Exercise 11.10, and using the 0.02 level of significance in comparing the sample standard deviations, were we justified in assuming that the population standard deviations are equal? Would your conclusion change if the standard deviation of playing times for music boxes equipped with the new battery design had been 20% larger than the value calculated in Exercise 11.10?
In exercise 11.10
In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows:

Assuming normal populations with equal standard deviations, use the 0.05 level to determine whether the new battery could be better than the old design. Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for this test?

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3.3, 6.4, 3.9, 5.4, 8 boxes, new battery type 5.1, 4.6, 4.9, 7.2 hrs 8 boxes, old battery type: 5.0, 5.1, 3.2, 4.0 hrs 4.2, 2.9, 4.5, 4.9,