(Solved): 4. [Sampling distribution, CLT] Let a random (and representative) sample of 314 IT startups is give ...

4. [Sampling distribution, CLT] Let a random (and representative) sample of 314 IT startups is given. According to the survey results, 218 enterpreneurs from the sample reported that inflation rate over the last year critically affected their business. (a) Find the sample proportion $\hat{p}$ of IT startups which were critically affected by the inflation rate. (b) Assuming the Central Limit Theorem is applicable, calculate the standard error for $\hat{p}$. (c) What is the probability that the sample proportion $\hat{p}$ of critically affected IT startups is smaller than population proportion $p$ ? (d) How likely is that the population proportion $p$ of critically affected IT startups is less than 0.75 ? (or, equivalently, but more accurately formulated, what is the probability that the sampling error $\hat{p}-p$ is larger than $0.056(=0.694-0.75)?)$