This is statistics course, sampling distributions, estimation and tests of significance .I need help with this. I attached formula sheet in case you need it.

II. Probability P(AUB) = P(A) + P(B) - P(An B) P(AB) = P(An B) P(B) E(X) = Ux = Expi Var(X) = 0; = _(x - ux)2pi If X has a binomial distribution with parameters n and p, then: P(X = k) = k) p* (1 - p)" -* HI = np Or = Vnp(1 - p) Ho = P Op = P(1- p n If x is the mean of a random sample of size n from an infinite population with mean u and standard deviation O, then: MY = HIII. Inferential Statistics Standardized test statistic: statistic - parameter standard deviation of statistic Confidence interval: statistic + (critical value) . (standard deviation of statistic) Single-Sample Statistic Standard Deviation of Statistic Sample Mean Sample Proportion p(1 - p) n Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 722 Special case when 61 =02 ol+1 n2 Difference of PI (1 - PI) + P2 (1 - P2) sample proportions n1 n2 Special case when P1 = P2 Jp(1 - P) 1 + 1 Vn, n2 Chi-square test statistic = \\ (observed - expected) expectedD Question 1 1 pts Which of these is NOT true regarding the Student's t-distribution discovered by William S. Goset? O are useful when sample sizes are small O are bell shaped O have less area under the tails than the standard normal distribution O as sample sizes increase, the distribution becomes more like the standard normal distribution there are n - 1 degrees of freedom, where n is the size of the sampleD Question 5 1 pts Suppose you decide to investigate the question below: Are more than 20% of Americans allergic to peanuts? You randomly survey 100 Americans asking "are you allergic to peanuts". Given a 5% level of significance, which of these is the least number of respondents that could say "yes" that would allow you to claim more than 20% of Americans are allergic to peanuts? 15 O 18 O 21 O 24 O 27