The results of a recent poll on the preference of voters regarding presidential

Question

The results of a recent poll on the preference of voters regarding presidential candidates are shown below. Candidate Voters Surveyed Voters Favoring This Candidate A 400 192 B 450 225 ? Using ? = .05, conduct a hypothesis test to determine whether or not there is a significant difference between the preferences for the two candidates.

A- The computed test statistic is _____________which has a p-value of___________

B- Will you reject the null hypothesis? Include yes or no in your response.

C- Is there sufficient evidence to conclude that there is a significant difference between the preferences for the two candidates? Include yes or no in your response.

Note: Use the probability distribution tables to find your p-values. If possible, report the exact p-value (to four decimal places). If an exact p-value is not available, report the smallest possible range for the p-value, using the following format when you report your answer: between lower limit p-value and upper limit p-value For example, enter into the answer box: between .01 and .02 (But report your p-values.)

Explanation / Answer

For Candidate A,

n1 = 400

y1 = 192

p1 (Proportion of voters voted for Candidate A) = 192/400 = 0.48

For Candidate B,

n1 = 450

y1 = 225

p2 (Proportion of voters voted for Candidate B) = 225/450 = 0.5

Overall Sample population = (192+225) / (400+450) = 0.4906 (approx.)

The Test statistic for testing is

H0 : p1=p2 versus H0 : p1 not = p2

Z = (p1-p2) / sqrt( p(1-p) (1/n1 + 1/n2) )

=> Z = -0.0583 - Ans 1

Now, considering Degree of freedom = 1, significance level = 0.05 with the above Z value

Gives us the p-value = 0.481464 which is greater than the significance level. - Ans 1

So, No we don't reject the null hypothesis, instead accept it. - Ans 2

So, we can conclude that there is not very significant difference between the preferences for the two candidates as p1 is equivalent to p2. - Ans 3

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.