Determining whether two samples are independent or paired a... A purchasing manager for a large university is deciding which brand of lights bulbs to purchase for classroom projectors. Of major concern is the longevity of the light bulbs. The purchasing manager has narrowed down the choice of light bulbs to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs. The purchasing manager obtained 12 Infocus bulbs and 14 Proxima bulbs for testing over the last several academic terms. (Consider these as random samples of the Infocus and Proxima bulbs.) The two samples were chosen separately, so that the selection of the Infocus bulbs did not affect the selection of the Proxima bulbs. The number of hours the bulbs lasted on each of the machines in the two samples were recorded. The following table gives the data, sample means, and sample standard deviations. Infocus 702, 879, 618, 893, 741, 723, 834, 1048, 887, 976, 707,745 Proxima 1001, 1035, 785, 927, 1045, 877, 721, 995, 1056, 1089, 1046, 856, 823, 780 Send data to calculator Lifetimes of light bulbs (hours) O independent samples O paired (dependent) samples Oz= 0 01 = 0 (a) Are the two samples of light bulbs independent or paired (dependent) samples? Choose the best answer. Explanation Sample mean Sample standard deviation 812.8 Check O 931.1 (b) The purchasing manager wants to use the data to determine whether the two brands differ in terms of the mean lifetime of the bulbs. Assume that both populations are approximately normally distributed. Choose the appropriate test statistic for the hypothesis test that would be performed. Then calculate that statistic. Carry your intermediate computations to three or more decimal places. Round your answer to three decimal places. (If necessary, consult a list of formulas.) 127.2 MacBook Pro 122.5 Ayishatu Español A) © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Access