Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

Upper H 0=0.6

versus

Upper H1​: >0.6

n=200​;

x=125​,

alphaα=0.1

Answer 1

Solution:

Here, we have to use z test for population proportion.

H₀: p = 0.6 versus H₁: p > 0.6

This is an upper tailed test.

We are given α = 0.1

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 = 125

n = sample size = 200

Sample size is adequate to use normal approximation.

p̂ = x/n = 125/200 = 0.625

p = 0.6

q = 1 - p = 0.4

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.625 – 0.6)/sqrt(0.6*0.4/200)

Z = 0.7217

P-value = 0.2352

(by using z-table)

P-value > α = 0.1

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the population proportion is greater than 0.6.