1. McDonalds sells “quarter pounder” hamburgers. Define as the average weight of

Question

1. McDonalds sells “quarter pounder” hamburgers. Define as the average weight of a quarter pounder measured in ounces. Consumer Reports believes that McDonalds is actually deceiving the public about the weight of their hamburgers. Set up the null and alternative hypotheses to support the Consumer Reports claim. 2. McDonalds hears about the Consumer Reports study and wants to sue for libel. Their lawyers suggest to first test another set of H0 and Ha hypotheses. Their lawyers want to go ahead with the libel-lawsuit if they can reject their null-hypothesis at = 0.05. What set of hypotheses would the McDonalds lawyers likely want to investigate? 3. Can you reject the lawyer’s null-hypothesis if a random sample of 100 hamburgers weighs 4.1 ounces and the population standard deviation equals 0.25 ounces? Use both a critical value and p-value approach.

Explanation / Answer

1. McDonalds sells “quarter pounder” hamburgers. Define as the average weight of a quarter pounder measured in ounces. Consumer Reports believes that McDonalds is actually deceiving the public about the weight of their hamburgers. Set up the null and alternative hypotheses to support the Consumer Reports claim.

Note that 1/4 lb = 4 oz.

By the word "deceiving", then they think the burgers are underweight. Hence,

Ho: u >= 4 oz
Ha: u < 4 oz [ANSWER]

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2. McDonalds hears about the Consumer Reports study and wants to sue for libel. Their lawyers suggest to first test another set of H0 and Ha hypotheses. Their lawyers want to go ahead with the libel-lawsuit if they can reject their null-hypothesis at = 0.05. What set of hypotheses would the McDonalds lawyers likely want to investigate?

They want to prove that the burgers are not underweight, so the null hypothesis is

Ho: u <= 4 oz
Ha: u > 4 oz [ANSWER]

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3.

Can you reject the lawyer’s null-hypothesis if a random sample of 100 hamburgers weighs 4.1 ounces and the population standard deviation equals 0.25 ounces? Use both a critical value and p-value approach.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   4  
Ha:    u   >   4  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    4.1          
uo = hypothesized mean =    4          
n = sample size =    100          
s = standard deviation =    0.25          
              
Thus, z = (X - uo) * sqrt(n) / s =    4          
              
Also, the p value is              
              
p =    3.16712*10^-5          
              
As z > 1.645, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Hence, there is significant evidence that the true mean weight of burgers is greater than 4 oz at 0.05 level. [CONCLUSION]

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