a) The gas mileage for a particular model car is known to have a standard deviat

Question

a) The gas mileage for a particular model car is known to have a standard deviation of = 1.0 mile per gallon in repeated tests in a controlled laboratory environment at a fixed speed. For a fixed speed, gas mileages in repeated tests are Normally distributed. Tests on three cars of this model at 65 miles per hour give gas mileages of 24.3, 24.9, and 24.8 miles per gallon. What is the z statistic for testing H0: = 25 miles per gallon based on these three measurements? (Round your answer to three decimal places.)

B) husband and wife, Ed and Rina, share a digital music player that has a feature that randomly selects which song to play. A total of 3476 songs have been loaded into the player, some by Ed and the rest by Rina. They are interested in determining whether they have each loaded different proportions of songs into the player. Suppose that when the player was in the random-selection mode, 36 of the first 52 songs selected were songs loaded by Rina. Let p denote the proportion of songs that were loaded by Rina. ( find the Z and p-value)

Explanation / Answer

(a) = 25, n = 3, x-bar = 24.67, = 1

SE = /n = 1/3 = 0.577350269

z = (x-bar - )/SE = (24.67 - 25)/0.577350269189626 = -0.572

(b) n = 52, x = 36, p' = 36/52 = 0.6923, p = 0.5

SE = {p (1 - p)/n} = (0.5 * (1 - 0.5)/52) = 0.0693

z = (p'- p)/SE = (0.692307692307692 - 0.5)/0.0693375245281536 = 2.7735

p- value = 0.0055

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