The pandemic in the past two years deeply impacted people’s life. A Covid-19 at-home self-tester is an excellent solution to reduce the risk of exposure effectively. A pharmaceutical company just developed new kinds of Covid self-tester. Answer the question below:

(a). Suppose the company used a computer simulation to determine the accuracy of their product. In a collection of 100 citizens, the tester revealed 67 correct results. Find a 93% confidence interval for this case.

(b). If one of their self-testers can detect the virus in 85% of cases. Suppose the company wants to use this tester in a new simulation for a sample of 500 citizens. How many correct detections (x) the tester needs to make to get a hypothesis test with alpha = 0.05 that support that alternative hypothesis? Present all possible values of x (using intervals