This is statistics course, sampling distributions, estimation and tests of significance units.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 6 1 pts Suppose an agent at the Internal Revenue Service (IRS) decides to use a hypothesis test to determine whether additional officers should be hired to investigate tax evasion. She decides to test whether the proportion of Americans who don't pay taxes is less than 0.15 and forms the following hypotheses: Ho: The proportion of Americans who don't pay taxes is at least 0.15. Ha: The proportion of Americans who don't pay taxes is less than 0.15. Select the appropriate description of a type I error in this context and a consequence of this type l error. O Failing to reject the null hypothesis when there actually was enough evidence to reject it. O She did not hire more officers, but the true proportion of Americans not paying their taxes is 0.15 or more. She hired more officers, but the true proportion of Americans not paying their taxes is less than 0.15. O Failing to reject the null hypothesis when it is actually false. O Rejecting the null hypothesis when it is actually false.D Question 7 1 pts A microchip factory manager decides to use a hypothesis test to determine whether additional money should be spent on quality control. He wishes to test the null hypothesis "Ho: the proportion of dysfunctional microchips is as least 0.10" against the alternative hypothesis "Ha: the proportion of dysfunctional microchips is less than 0.10". Describe a type II error in this context and a consequence of this error. The manager doesn't reject the null hypothesis, but it was false. He ends up selling more defective chips than he expected to. The manager doesn't reject the null hypothesis, but it was false. He spends money on quality control that was not needed. The manager rejects the null hypothesis, but it was true. He ends up selling more defective chips than he expected to. The manager rejects the null hypothesis, but it was true. He spends money on quality control that was not needed. O The manager rejects the null hypothesis, and it was false. He ends up selling more defective chips than he expected to.
