Question

Businesses are always looking for new ways to draw attention to their products. A new ketchup...

Businesses are always looking for new ways to draw attention to their products. A new ketchup company is considering producing purple ketchup. Since producing purple ketchup is very costly, the company stands to lose a lot of money if less than 20% of all adults would purchase the ketchup. However, if more than 20% of adults would purchase the ketchup, the company would make a fortune.

(a) Define the parameter of interest and state the null and alternative hypotheses that the ketchup company should test.

(b) In the context of this situation, describe Type I and Type II errors and describe the consequences of each of those for the ketchup company.

Math   Statistics-And-Probability   
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Answer #1

a) parameter of interest is proportion of adults who would purchase the ketchup

Ho :   p =    0.2
H1 :   p >   0.2

b)

Type I error is concluding that company would make a fortune while in fact , the company stands to lose a lot of money

This is very serious error as company will lose lots of money because  in actual less than 20% of all adults would purchase the ketchup.

Type II error is concluding that the company stands to lose a lot of money , while in fact company would make a fortune.

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