A student wants to assess whether her dog Muffin tends to chase her blue ball mo

Question

A student wants to assess whether her dog Muffin tends to chase her blue ball more often than she chases her red ball. The student rolls both a blue ball and a red ball at the same time and observes which ball Muffin chooses to chase. Repeating this process a total of 96 times, the student finds that Muffin chased the blue ball 57 times and the red ball 39 times.

1. What proportion of the 96 toss did Muffin chase the blue doll? use appropriate symbols

2. Estimate pi using a 95% confident level.

3. Is this number from a parameter or a statistic. Explain

Explanation / Answer

1.

Note that              
              
p^ = point estimate of the population proportion = x / n = 57/39 =   0.59375 [ANSWER]

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2.           
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.050125981          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.098245117          
lower bound = p^ - z(alpha/2) * sp =   0.495504883          
upper bound = p^ + z(alpha/2) * sp =    0.691995117          
              
Thus, the confidence interval is              
              
(   0.495504883   ,   0.691995117   ) [ANSWER]

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3.

The answer in part 2 is a PARAMETER, because it describes the population proportion. [ANSWER]

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