Question

A random sample of n = 1,500 observations from a binomial population produced x = 413.

If your research hypothesis is that p differs from 0.3, calculate the test statistic and its p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

Answer 1

Solution:

One sample z test for population proportion

H₀: p = 0.3 versus H_a: p ≠ 0.3

Test statistic formula for this test 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

x = number of items of interest = 413

n = sample size = 1500

p̂ = x/n = 413/1500 = 0.275333333

p = 0.3

q = 1 - p = 0.7

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.275333333 – 0.3)/sqrt(0.3*0.7/1500)

Z = -2.0847

Test statistic = -2.08

P-value = 0.0371

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis at 5% level of significance.