Question

One of the two fire stations in a certain town responds to calls in the northern half of the town, and the other fire station responds to calls in the southern half of the town. The following is a list of response times (in minutes) for both of the fire stations (this data will be used for several problems). Both samples may be regarded as simple random samples from approximately normal populations so that the t- procedures are safe to use. Northern: 3,3,3,3, 4.4.4.4.4.5, 5, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10.12 Sum = 192 Sum of Squared Deviations = 197.2 Southern: 4, 4, 4, 4, 5, 5, 5.5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 12, 12, 12, 12, 13 Sum = 225 Sum of Squared Deviations = 231.5 Find and interpret a 95% confidence interval for the mean response time of the fire station that responds to calls in the northern part of town. Fill in blank 1 to report the bounds of the 95% CI. Enter your answers as lower bound upper bound with no additional spaces and rounding bounds to two decimals Blank #1: 95% confident that the true mean response time of the fire station in the northern part of town is between and _minutes Blank #2: If you had not been told that the sample came from an approximately normally distributed population, would you have been okay to proceed in constructing the interval given in blank #1? Why? Choose the best response as described below and enter your answer as 1.2.3 or 4. (1) no the distribution is not symmetric and the sample size is not large (2) no the distribution is extremely skewed even though the sample size is large (3) yes the distribution is only slightly skewed and the sample size is large (4) yes the t-procedures are always safe to use Blank # 1 Blank # 2

Answer 1

.) interval is given 957 confidence by sc I s tan- มาก 2 = Esci n=30 192 30 11 6.4 Se ( Exci Exci² – nã nx²) or ng - Elxi-x2 na 2.6077 6.4 I 2.6077 X 2.045 J 30 6.4 - D. 9736 (5.4264 7.3736 2 2) Yes the skewed distribution is only slightly Sample size is large and