Question

A research center claims that more than 32​% of employees in a certain country have changed jobs in the past four years. In a random sample of 340 people from that​ country, 119 have changed jobs in the past four years. At alpha equals 0.01​, is there enough evidence to support the​ center's claim? Complete parts​ (a) through​ (e) below. a) Identify the claim and state Upper H 0 and Upper H Subscript a. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). ​(c) Find the standardized test statistic z. (d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Answer 1

a) As we are testing here whether the proportion of employees who changed jobs is more than 0.32, therefore the null and the alternate hypothesis here are given as:

b) As this is an upper tailed test, we get from the standard normal tables that:

P(Z < 2.326) = 0.99

Therefore P(Z > 2.326) = 0.01

Therefore 2.326 is the required critical value here.

c) The sample proportion here is computed as:
p = x/n = 119/340 = 0.35

Therefore the test statistic here is computed as:

Therefore 1.1859 is the required test statistic value here.

d) As the test statistic value here is less than 2.326, therefore it lies in the non rejection region. Therefore do no reject H₀ is the correct answer here.

e) This shows that we dont have sufficient evidence here that more than 32​% of employees in a certain country have changed jobs in the past four years.