(1 point) A certain airline wishes to estimate the mean number of seats that are empty on flights that use 737-airplanes. There are 189 seats on a 737. To do so, the airline randomly picks n = 35 flights. For each flight, the number of empty seats is counted. The data are given below. 57, 45, 52, 53, 55, 40, 36, 52, 47, 37, 40, 45, 51, 41, 54, 34, 52, 55, 41, 46, 42, 50, 49, 35, 55, 40, 52, 37, 55, 56, 44, 48, 49, 48, 47 Data from the sample, are saved in the Download .csv fil. Distribution of Empty Seats 10 Frequency N_- - o I I I I I I I 30 3 5 4O 45 50 55 60 Number 01 Unooeupied Seals (a) Find the mean and the standard deviation of this sample. Use at least three decimal places in each answer. 17' = 46.8571428! 555 emptyseats S = 675688257: 555 empty seats (b) To construct a confidence interval for the mean number using the T distribution for unoccupied seats on all flights that use 7375, what condition must you hold? OA. That the number of unoccupied seats are normally distributed. Q) B. The sample size is sufficiently large for the Central Limit Theorem to provide a valid approximation. 0 C. The number of unoccupied seats can be modeled by the Binomial distribution. 0 D. The number of unoccupied seats are not normally distributed. (c) Find a 96% Student T confidence interval for u, the mean number of empty seats on this airline's flights that use 7375. Use at least three decimal points for your lower and upper bounds. To avoid rounding errors you should use R-Stuido and not Tables. Lower Bound: 2.43909404: iii empty seats Upper Bound = 46.857143 EEE empty seats (d) Find a 96% confidence interval for ,u, the mean number of empty seats on this airline's flights that use 7375, by Bootstrapping 1000 samples. Use the seed 7733 to ensure that R-Studio "randomly" samples the same "random" samples as this question will expect. You can do this by including the code, you can copy it into your RStudio to bootstrap your samples. RNGkind(sample.kind="Rejection"); set.seed(7733); B=do(1000) * mean(resample(c(57, 45, 52, 53, 55, 40, 36, 52, 47, 37, 40, 45, 51, 41, 54, 34, 52, 55, 41, 46, 42, 50, 49, 35, 55, 40, 52, 37, 55, 56, 44, 48, 49. 48. 47), 35)); Ignore any errors or warnings that show up. Use at least three decimal points for your lower and upper bounds. Lower Bound = 49.296236 EEE empty seats Upper Bound= 44.418049 555 empty seats 57 2 45 3 52 53 5 55 6 40 36 8 52 47 10 37 11 40 12 45 13 51 14 15 54 16 34 7 52 18 55 19 41 20 46 21 42 22 50 23 49 24 35 25 55 26 40 27 52 28 37 29 55 30 56 31 44 32 48 33 49 34 48 35 47
