For an experiment on influencing the choices of others by offering undesirable​ alternatives, each of 103 college students selected three portable grills from five to display on a showroom floor. The students were instructed to include Grill​ #2 (a​ smaller-sized grill) and select the remaining two grills in the display to maximize purchases of Grill​ #2. If the six possible grill display combinations​ (1-2-3, 1-2-4,​ 1-2-5, 2-3-4,​ 2-3-5, and​ 2-4-5) were selected at​ random, then the proportion of students selecting any display was 1/6=0.167. One theory tested by the researcher was that the students would tend to choose the​ three-grill display so that Grill​ #2 was a compromise between a more desirable and a less desirable grill​(that is, display​ 1-2-3, 1-2-4, or​ 1-2-5). Of the 103 students, 57 selected a​ three-grill display that was co

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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For an experiment on influencing the choices of others by offering undesirable​ alternatives, each of 103 college students selected three portable grills from five to display on a showroom floor. The students were instructed to include Grill​ #2 (a​ smaller-sized grill) and select the remaining two grills in the display to maximize purchases of Grill​ #2. If the six possible grill display combinations​ (1-2-3, 1-2-4,​ 1-2-5, 2-3-4,​ 2-3-5, and​ 2-4-5) were selected at​ random, then the proportion of students selecting any display was 1/6=0.167. One theory tested by the researcher was that the students would tend to choose the​ three-grill display so that Grill​ #2 was a compromise between a more desirable and a less desirable grill​(that is, display​ 1-2-3, 1-2-4, or​ 1-2-5). Of the 103 students, 57 selected a​ three-grill display that was consistent with this theory. Use this information to test the theory proposed by the researcher at α=0.01.

 

1. Identify the test​ statistic, z.
​(Round to two decimal places as​ needed.)
 
2. Find the observed significance level of the test.
​(Round to three decimal places as​ needed.)
State the conclusion for this hypothesis test.
 
3. Do not/Reject H0. There is/is not sufficient evidence at the α=0.10 level of significance to conclude that the proportion of students who select a​ three-grill display that is consistent with the compromise theory is not equal to/less than/greater than 0.5.
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