Test statistic for college student

Question

Testing:

H0:p=0.3

H1:p<0.3

Your sample consists of 131 subjects, with 36 successes. Calculate the test statistic, rounded to 2 decimal places

Answer 1

Assuming conditions are met, we can calculate the z-statistic:

z = (p̂-p₀)/√[p₀(1-p₀)/n] = (36/121 - 0.3)/√[0.3(1-0.3)/131] ≈ -0.06

Also, assuming a significance level of α=0.05:

P(Z<z) = P(Z<-0.06) ≈ 0.4761 > 0.05

Hence, we fail to reject the null hypothesis, which tells us that the true population proportion is most likely less than p=0.3

Hope this helped!