A student wants to assess whether her dog Muffin tends to ch

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 196 times, the student finds that Muffin chased the blue ball 102 times and the red ball 94 times.

a. What are the observational units in this study?   

b. What is the variable in this study?

c. State the appropriate null and alternative hypotheses, in words and in symbols.

d. Calculate the test statistic and p-value.

e. Would you reject the null hypothesis at the .10 significance level? Explain.

f. Write a one-sentence conclusion to the student, summarizing what the data reveal about whether her dog Muffin tends to chase her blue ball more often than her red ball. Include an explanation of what the p-value means in the context of this study.

Solution

a) To observe whether her

b) Blue Ball, and the red ball

c)Test For Difference in Proportion

Null Hypothesis, dog Muffin tends to chase her blue ball

more often than she chases her red ball Ho: p1 > p2

Alternate Hypothesis, H1: p1 < p2

d)

Test Statistic

Sample 1 : X1 =102, n1 =196, P1= X1/n1=0.5204

Sample 2 : X2 =94, n2 =196, P2= X2/n2=0.4796

Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)

P^=0.5

Q^ Value For Proportion= 1-P^=0.5

we use Test Statistic (Z) =   (P1-P2)/?(P^Q^(1/n1+1/n2))

Zo =(0.52-0.4796)/Sqrt((0.5*0.5(1/196+1/196))

Zo =0.8081Critical Value

The Value of |Z ?| at LOS 0.1% is 1.282

We got |Zo| =0.808 & | Z ? | =1.282

e)

Make Decisiona

Hence Value of |Zo | < | Z ? | and Here we Do not Reject Ho

P-Value: Left Tail - Ha : ( P < 0.8081 ) = 0.79049

Hence Value of P0.1 < 0.79049,Here We Accept Ho

f)

We conclude that Muffin tends to chase her blue ball more often than her red ball