Question

From previous studies, it is concluded that 40% of workers indicate that they are mildly dissatisfied with their job. A researcher claims that the proportion is smaller than 40% and decides to survey 400 working adults. Test the researcher's claim at the α=0.01 significance level.

Preliminary:

1. Is it safe to assume that n≤0.05 of all subjects in the population?
   • No
   • Yes
   
   
2. Verify np(1−p)≥10. Round your answer to one decimal place.
   
   np(1−p)=

Test the claim:

1. The null and alternative hypotheses are
   • H0:p≥0.4
     Ha:p<0.4
   • H0:p≤0.4
     Ha:p>0.4
   • H0:μ≤0.4
     Ha:μ>0.4
   • H0:μ=0.4
     Ha:μ≠0.4
   • H0:p=0.4
     Ha:p≠0.4
   • H0:μ≥0.4
     Ha:μ<0.4
   
   
2. The test is
   Select an answer two-tailed left-tailed right-tailed
3. Based on the sample of 400 people, 35% workers indicate that they are mildly dissatisfied with their job. What is the test statistic? Round your answer to two decimal places.
   ? z= t=  
   
4. What is the pp-value? Round your answer to four decimal places.
   
   
5. Make a decision.
   • Reject the null hypothesis.
   • Do not reject the null hypothesis.
   
   
6. Make a conclusion.
   • There is not sufficient evidence that the proportion of people who workers indicate that they are mildly dissatisfied with their job is smaller than 40% at the α=0.01 significant level.
   • There is sufficient evidence that the proportion of people who workers indicate that they are mildly dissatisfied with their job is smaller than 40% at the α=0.01 significance level.

Answer 1