Question

Many smartphones, especially those of the LTE-enabled persuasion, have been criticized for exceptionally poor battery life. Battery life between charges for the Motorola Droid Razr Max averages 20 hours when the primary use is talk time and 7 hours when the primary use is Internet applications (The Wall Street Journal, March 7, 2012). Since the mean hours for talk time usage is greater than the mean hours for Internet usage, the question was raised as to whether the variance in hours of usage is also greater when the primary use is talk time. Sample data showing battery hours of use for the two applications follows. Click on the datafile logo to reference the data. DATA file 22.2 3.8 4.0 30.0 32.6 12. 8 8.5 1 0.3 42.5 35.5 Primary Use: Talking 35.8 8.0 Primary Use: Internet 14.0 5.4 12.5 16.4 1.9 9.9 1.0 15.2 4.0 4.7 a. Formulate hypotheses about the two population variances that can be used to determine if the population variance in battery hours of use is greater for the talk time application. Ho : 01" - Select your answer - 02 H :01 - Select your answer - 024 b. What are the standard deviations of battery hours of use for the two samples? Round your answers to two decimal places. -$1 = -$2 = c. Conduct the hypothesis test and compute the p-value. The value of Fis (to 2 decimals) p-value is (to 4 decimals) Using a .05 level of significance, what is your conclusion?

Answer 1

a) Ho: σ₁² = σ₂²
Ha: σ₁² > σ₂²

b) For talking,

	X	(X-mu)	(X-mu)*(X-mu)
	35.8	15.3	234.09
	22.2	1.7	2.89
	4	-16.5	272.25
	32.6	12.1	146.41
	8.5	-12	144
	42.5	22	484
	8	-12.5	156.25
	3.8	-16.7	278.89
	30	9.5	90.25
	12.8	-7.7	59.29
	10.3	-10.2	104.04
	35.5	15	225
Mean	20.5	Sum	2197.36
		Standard Deviation	14.13365

s1 = 14.13

For internet,

	X	(X-mu)	(X-mu)*(X-mu)
	14	5.5	30.25
	12.5	4	16
	16.4	7.9	62.41
	1.9	-6.6	43.56
	9.9	1.4	1.96
	5.4	-3.1	9.61
	1	-7.5	56.25
	15.2	6.7	44.89
	4	-4.5	20.25
	4.7	-3.8	14.44
Mean	8.5	Sum	299.62
		Standard deviation	5.769845

s2 = 5.77

c) F-statistic = s₁²/s₂² = 14.13² / 5.77² = 6.00 (rounded to two-decimal places)

d) df1 = 12 - 1 = 11

df2 = 10 - 1 = 9

p-value = 0.0060

e) As the p-value < 0.05, we can reject the null hypothesis. We conclude that population variance in battery hours of use for talking is greater for talk time application