From previous studies, it is concluded that $12 \%$ of workers indicate that they are satisfied with their job. A researcher claims it has decreased and decides to survey 100 adults. Test the researcher's claim at the $a=0.05$ significance level. Verify $n p^{\wedge}\left(1-p^{\wedge}\right) \geq 10$. Round your answer to one decimal place.
Answer
Final Answer: \(\boxed{10.56}\)
Step 1 ：Given that the sample size n = 100 and the proportion of workers who are satisfied with their job p = 0.12.
Step 2 ：Calculate the value of \(n p^{\wedge}\left(1-p^{\wedge}\right)\) to verify if it is greater than or equal to 10.
Step 3 ：The calculated value of \(n p^{\wedge}\left(1-p^{\wedge}\right)\) is 10.56, which is greater than 10.
Step 4 ：Therefore, the sample size is large enough to perform a hypothesis test.
Step 5 ：Final Answer: \(\boxed{10.56}\)
