Question

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

H0​: p=0.4 versus H1​: p>0.4

n=125​; x=55, a=0.05

Use technology to find the​ P-value.

​P-value=_________

​(Round to three decimal places as​ needed.)

Answer 1

Solution:

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

H₀: p = 0.4 versus H_a: p > 0.4

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

x = 55

n = 125

p = 0.4

q = 1 – p = 1 – 0.4 = 0.6

p̂ = x/n = 55/125 = 0.44

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.44 – 0.4)/sqrt(0.4*0.6/125)

Z = 0.9129

P-value = 0.181

(by using excel)

P-value > α = 0.05

So, we do not reject the null hypothesis