A local election is being held, and the primary issues revolve around public sch

Question

A local election is being held, and the primary issues revolve around public schools.In one school district, 40 of 60 randomly selected voters said that they would vote for candidate A.In another school district, 36 of the 60 randomly selected voters said they planned to vote for that same candidate A.Is there a statistically significant difference between candidate A’s percentage of likely voters in the two school districts at the 0.01 significance level? Perform a full hypothesis test and show your work.

Explanation / Answer

Solution:

Here, we have to use the z test for two population proportions. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any statistically significant difference exists between the candidate A’s percentage of likely voters in the two school districts.

Alternative hypothesis: Ha: There is a statistically significant difference exists between the candidate A’s percentage of likely voters in the two school districts.

H0: p1 = p2 versus Ha: p1 p2

We are given level of significance = = 0.01

For first group

X1 = 40

N1 = 60

P1 = 40/60 = 0.67

For second group

X2 = 36

N2 = 60

P2 = 36/60 = 0.60

The test statistic formula is given as below:

Z = (P1 – P2) / sqrt[(P1Q1/N1)+(P2Q2/N2)]

Where, Q1 = 1 – P1= 1 – 0.67 = 0.33 and Q2 = 1 – P2 = 1 – 0.60 = 0.40

Z = (0.67 – 0.60)/sqrt((0.67*0.33/60)+(0.60*0.40/60))

Z = 0.798502

Critical value = 2.5758 and -2.5758

P-value = 0.4246

= 0.01

P-value > = 0.01

So, we do not reject the null hypothesis that there is no any statistically significant difference exists between the candidate A’s percentage of likely voters in the two school districts.

We conclude that there is sufficient evidence that there is no any statistically significant difference exists between the candidate A’s percentage of likely voters in the two school districts.

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