Question

In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were: In a certain city, there are about one million eligible voters.

	Men	Women
Voted	2499	3311
Didn't Vote	1722	2468

If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH₀) or Failure to Reject (FRH₀)] If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]

a) [p-value = 0.056, FRH₀]

b) [p-value = 0.301, FRH₀]

c) [p-value = 0.056, RH₀]

d) [p-value = 0.301, RH₀]

e) [p-value = 0.028, RH₀]

Answer 1

SOLUTION:

From given data,

A simple random sample of size 10,000

Add up rows and columns:

	Men	Women	Total
Voted	2499	3311	5810
Didn't Vote	1722	2468	4190
Total	4221	5779	10000

Calculate "Expected Value" for each entry:

Multiply each row total by each column total and divide by the overall total:

	Men	Women
Voted	5810*4221 / 10000 = 2452.401	5810*5779 / 10000 = 3357.599
Didn't Vote	4190*4221 / 10000 = 1768.599	4190*5779 / 10000 = 2421.401

Subtract expected from actual, square it, then divide by expected:

=

	Men	Women
Voted	(2499-2452.401)2 / 2452.401 =0.885445	(3311-3357.599)2 / 3357.599 =0.646732
Didn't Vote	(1722-1768.599)2 / 1768.599 =1.227789	(2468-2421.401)2 / 2421.401 = 0.896781

Now add up those values:

0.885445+0.646732+1.227789+0.896781 = 3.656747

Chi-Square = = 3.656747

From Chi-Square to p

Calculate Degrees of Freedom

= (rows − 1) (columns − 1)

DF = (2 − 1)(2 − 1) = 1×1 = 1

P- value at   = 3.65674 with   DF = 1

P- value = 0.05584280

approx , P- value = 0.056

at 5% significance level that is

= 0.05

P- value >

Failure to Reject null hypothesis

Answer is a) [p-value = 0.056, [FRH₀]