Chi-squared goodness of fit test to determine if box colors are not equally likely using a=0.05.
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Use the following scenario for questions 1) and 2):
An automobile manufacturer buys radios to install in their vehicles. Each radio is packaged in
a box within a large shipping container. One of the employees who installs radios noticed that
the individual radio boxes come in three colors: Blue, Green, and Red. The employee
assumes that the box colors are equally likely. To assess this assumption, the employee
collects a random sample of 30 boxes. The box color is recorded and the data are summarized
in the frequency table below (Radio Box Color worksheet). The employee uses a Chi-squared
goodness of fit test to determine if box colors are not equally likely using a=0.05.
1) What is the test statistic for the hypothesis test?
A) 0.8
B) 8
C) 10
D) 0.4
E) 30
2) What is the critical value for the hypothesis test?
A) 3.841
B) 5.991
C) 7.815
D) 40.11
E) 42.56
3) A market research analyst wanted to determine if the proportion of mayonnaise
purchasers who were loyal to their favorite brand (PM) is different than the proportion
of bath soap purchases who were loyal to their favorite brand (Ps). Specifically, the
analyst wants to test the hypothesis Ho: PM = Ps versus Ha: PM ‡ Ps. A survey of
100 mayonnaise purchasers showed that 65 were loyal to their favorite brand and a
survey of 100 bath soap (S) purchasers showed that 53 were loyal to their favorite
brand (Brand Proportion worksheet). What is the test statistic for the hypothesis test?
A) 0.12
B) 0.59
C) 1.73
D) 2.30
E) 2.44
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