Question

The government conducts a survey of the population and finds that 111 of 536 respondents report voting for party A last election, and 114 of 745 respondents report voting for party A for the next election. If you are conducting a hypothesis testing with a null hypothesis of p1=p2 calculate the test statistic (z score) for this test where you are testing for p1-p2, where p1 and p2 represent the propportions from last election and this election, respectively

Answer 1

Z = 2.5088

Solution:

Here, we have to use z test for difference in population proportions.

H₀: p₁ = p₂ versus H_a: p₁ ≠ p₂

The test statistic formula is given as below:

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Where,

X1 = 111

X2 = 114

N1 = 536

N2 = 745

P = (X1+X2)/(N1+N2) = (111 + 114) / (536 + 745) = 0.1756

P1 = X1/N1 = 111/536 = 0.207089552

P2 = X2/N2 = 114/745 = 0.153020134

Z = (P1 – P2) / sqrt(P*(1 – P)*((1/N1) + (1/N2)))

Z = (0.207089552 – 0.153020134) / sqrt(0.1756*(1 – 0.1756)*((1/536) + (1/745)))

Z = 0.054069418/ sqrt(0.1756*(1 – 0.1756)*((1/536) + (1/745)))

Z = 2.5088

P-value = 0.0121

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a significant difference in the proportions of respondents who report voting for party A from last election and this election.