Question 1181946: The ABM Coffee Company claims that 20% of the coffee drinkers in Pinalagad, Malinta prefer their brand, the Ang Barako Mo coffee. To test the claim, a group of CNHS Grade 11 students conducted a survey, which they found out. Out of the 500 randomly selected residents, 95 indicated that ABM coffee is the reason why they wake up in the morning. Set up the Rejection Region and the Critical Values for Left-Tailed, Right-Tailed, and Two-Tailed tests. Use ɑ=.10.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: ABM has 20% preference
Ha: ABM does not have 20% preference (2-tailed) and critical value |z|>1.645.
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Ho: ABM has less than or =20% preference
Ha: ABM has > 20% preference (right-tail) with critical value z>1.282
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Ho: ABM has greater than or equal to 20% preference.
Ha: ABM has < 20% preference (left-tail) with critical value z < -1.282
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I learned hypothesis tests in that both have to cover the entire possibility, and that generally equal goes with the null hypothesis.
Also, the direction of the data should be noted. Here, the percentage is 19%, so one would expect the alternative hypothesis to be < 20% OR not equal to 20%. If the alternative hypothesis is greater than 20%, the data don't show it a priori.
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The equation is z=(p hat-p)/sqrt(0.2*0.8/500)
=-0.01/sqrt(.16/500)
=-0.559
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