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 52 times and the red ball 44 times.

a. Identify the observational units?

b. Identify 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 a=.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.

Answer 1

Given:

Sample 1 :

X1 = 52, n1 =96,

Sample 2 : X2 = 44 , n2 =96,

Sample proportion:

1 = X1/n1 = 52/96 = 0.5417

2 = X2/n2 = 44/96 = 0.4583

Pooled proportion, = X1+X2/n1+n2 = 52+44/96+96 = 0.5

(a) The observational units in this study is red and blue balls.

(b) The variable in this study is the number of times blue ball chase by dog muffin.

(c) Hypothesis test:

In word:

H0 : There is no difference in the proportion of Blue and Red balls chased.

Ha: Proportion of Blue balls chased is greater than that of Red balls.

Ho: p1 p2

H1: p1 > p2

d) Test statistics is

f) We may conclude that the data does not provide sufficient evidence to support the claim that the student's dog Groot tends to chase her blue ball more often than she chases her red ball.