Question

On a television show eight contestants try to lose the highest percentage of weight in order to win a cash prize As part of the show, the contestants are timed as they run an obstacle course. The table shows the times in seconds) of the contestants at the beginning of the season and at the end of the season. At a = 0.01, is there enough evidence to support the claim that the contestants times have changed? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Contestant 1 2 3 4 5 6 7 8 Time (beginning) 106.7 144.9 1054 155 21104121213041374 Time (end) 106.4 145.1 1053 155. 4 110 2 121.11389 136.9 (a) Identify the claim and state Ho and H What is the claim? O A. The contestants' times have increased ortO B . The contestants times have decreased OC. The contestants' times have changed ansO D. The contestants' times have not changed. W H and H.?

Answer 1

from Beginning 1067 En 144.9 105.4 the given data, we have - End di = Beginning- End 106.4 +03 145.1 -02 105.3 155.4 -0.2 110.2 +0.2 +01 155.2 110.4 +0.1 121.2 138.4 137.4 121.1 138.9 -0.5 +0.5 136.9 Z di = +0.3 d = Edit +03 +0.0375 Sony E (di-aj? Eve11-.3 – 0.137.52 ...-0.50.037972 = 0.3204 (0) Claim @ The contestan is limes have changed b) Hypothesis Hoild = 0 Ho: Mo 70 (E) correct option This is a two failed tere

(b) Critical value a = 0.01 Alp=0.005 degree of freedom (df) = no -87-7 Horiticas = $0.006,7 = + 3.5 A ! <F357 > 13.5 Rejechon Region Resechon Region +3.5 -3.5 (c đ = 0.0375 sa = 0.3204 (d) Test statistics . 0.0375 0.0375 ta d a 0.3204/18 A 30 = 0.3310 = 10.3317 Round to three decimal places (e) since Israt does not wie in the rejection Region so fail to Reject the nee Hypothesis. Trail to Reject the null hypothesis. There is not enough evidence to support the claim that the contestant's times have fnot changed
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