Problem 5.15 (MT-IB 1997-203G short) Explain what is meant by a sufficient statistic. Consider the independent RVs X,, X,. ..., X„, where X,~ N(a+ Bc,. 0) for given constants c,, i=1, 2, ..., n, and unknown parameters a, ß and 0. Find three sample quantities that together constitute a sufficient statistic.

14) Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is u, = 0. Compute the value of the t test statistic. Round %3D intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. х 28 31 20 25 28 27 33 35 26 27 26 25 29 32 33 34 A) t =-1.480 B) t=-1.185 C) t = -0.523 D) t= 0.690 %3D

An apple orchard farmer wants to know the true population proportion of all apples harvested at their farm which have the less valuable condition of being blemished, or in other words, are cider apples. This true population proportion is a parameter value represented by the symbol p. As a population parameter, this value can never be known with certainty. It can however, be estimated with varying levels of confidence. To estimate this parameter p, the farmer draws a simple random sample (SRS) of 524 apples from the orchard. Within this sample, the farmer finds that exactly 47 of the apples are cider apples. The farmer then computes a 96%-level confidence interval estimate for the parameter p. In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Lower Limit of this confidence interval? Include a percentage symbol at the end of your numerical answer (with no spaces).

26. In a two-tailed hypothesis about a population mean with a random sample size of 100 and a 0.05 level of significance, which of the following describes the appropriate critical region? А. z > 1.645 В. z 1.645 z 1.96 С. D. z > 1.96