Question

14. The Census Bureau wants to conduct a survey to determine the percentage ofadults that buy clothing online. How many adults do they need to survey in order to be confident that the sample proportion is in error by no more that 2 percentage points. 15. An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability that it will not be enough seats to accommodate all passengers. Assume that the probability that a randomly selected passenger shows up to the airport is 0.96. Find the probability using the normal distribution as an approximation to the binomial distribution 16. Explain in detail the meaning of P-Value? 17. What is the meaning of Type 1 error in Hypothesis Testing? 18. What is the meaning of type II error in Hypothesis Testing? 19. Explain when do we use the t-distribution rather than the standard normal distribution 20. Explain what is the meaning of being 99% confident when we estimate the population mean with a sample mean

Answer 1

14. p = 0.5

E = 0.02

z = 1.96

n = (z/E)2*p*(1 - p)

n = (1.96/0.02)2*0.5*(1 - 0.5)

n = 2401

15. µ = n*p = 300*0.96 = 288

σ = √n*p*(1 - p) = √300*0.96*(1 - 0.96) = 3.39

Required probability = (320 - 288)/3.39 = 5.9

P(z = 5.9) = 1.0000

16. In statistical hypothesis testing, the p-value or probability value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct.

17. In statistical analysis, a type I error is the rejection of a true null hypothesis, whereas type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false. In other words, it produces a false positive. The error rejects the alternative hypothesis, even though it does not occur due to chance.

18. A type II error is a statistical term referring to the non-rejection of a false null hypothesis. It is used within the context of hypothesis testing.

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