Question

hello, I was wondering if I can see an example of a statistics prop1ztest. and a bit more information about when to use it.

Answer 1

We use one sample z test for the population proportion when we have to prove any claim about the single population proportion. Suppose we have to check or test the claim whether majority of students use their own vehicles to reach the school. This means we have to check whether the proportion of the students who use their own vehicles to reach the school is greater than 50% or not. For checking this hypothesis or claim we need to use one sample z test for the population proportion. From randomly selected 50 students, it was observed that 31 students use their own vehicles for reaching the school. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: No majority of students use their own vehicles to reach the school.

Alternative hypothesis: H_a: Majority of students use their own vehicles to reach the school.

H₀: p ≤ 0.50 versus H_a: p > 0.50

This is an upper tailed or right tailed (one tailed) test.

We assume level of significance = α = 0.05 for this test.

The test statistic formula is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

p̂ = x/n

x = number of items of interest

We are given

x = 31

n = 50

p̂ = x/n = 31/50 = 0.62

p = 0.50

q = 1 – 0.50 = 0.50

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.62 - 0.50)/sqrt(0.50*0.50/50)

Z = 1.697056

P-value = 0.044843

(by using z-table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that Majority of students use their own vehicles to reach the school.