answer all questions with explanation

A company has a plant that produces airbags. The manager of the company believes that the plant produces at most a fraction 0.1 of defective airbags. To check if this is the case, she collects a sample of 500 observations and calculates a sample proportion of p - 0.08. The test for the manager's hypothesis is Hop - 0.1 and she wants to have a significance level a = 0.05. [Note: it would be helpful to draw a picture/curve to guide your analysis.] 1. (1 point) Compute the bound(s) of the rejection region and the value of the test statistic for this test. 2. (1 point) Can you reject the null hypothesis? 3. (1 point) Now suppose you use significance level o - 0.1 instead. Can you reject the null hypothesis? Show your computations and explain. 4. (1 point) Now suppose you use significance level a - 0.01 instead. Can you reject the null hypothesis? Show your computations and explain. 5. (2 points, relatively difficult) Now suppose the manager can increase the sample size (from 500 to a larger number). Suppose the sample proportion p = 0.08 remains the same in the enlarged sample. If she aims to reject the null hypothesis at o = 0.01 (so that she can support the alternative hypothesis), at least how large the enlarged sample size should be