Question

An executive believes that no more than 80% of the company’s employees take all of their vacation days. In a sample of 197 members, 136 employees took all of their vacation days. When testing the executive's hypothesis (using a 1% level of significance), what is the test statistic? (please round your answer to 2 decimal places)

Answer 1

Solution:

The test statistic formula for the required z test for population proportion 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 = 136

n = 197

p̂ = x/n = 136/197 = 0.690355

p = 80% = 0.80

q = 1 – p = 1 – 0.80 = 0.20

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.690355 - 0.80)/sqrt(0.80*0.20/197)

Z = -3.84735

Test statistic = Z = -3.85