Please try!, all the parts and the three questions, not miss any, Thanks !

1) The sample standard deviation is a random variable, why is this? Is the population standard deviation a random variable? Tutorial 6. No18) Of a random sample of 250 economics students across several universities, 180 claimed that exaggerating one's CV is unethical. Based on this information, a statistician computed a confidence interval extending from 0.68 to 0.76. What confidence level was used to construct this confidence interval? ANSWER: The width of the confidence interval is 0.08, implying a margin of error of 0.04. The sample proportion is 180/250 = 0.72. Plugging in what we know... 0.72(0.28) 0.04 = Za/2 250 Za/2 = 1.41 We can now calculate a: a = 2 x [1 - F2 (1.41)] = 2 x [0.0793] = 0.1586 The confidence level was 100 x (1-0.1586)%=84.14% The last few lines from Z alpha/2=1.41 and that calculation about alpha, how is this arrived and what does Fz(1.41) mean? Where did they get the 0.0793 from?and how was the confidence level worked out etc?Explain the answer, how do you the sample variance refers to chi-square distribution? ls chi- square distribution not symmetric and why? When constructing condence intervals for a population mean or for a population proportion, the general formula is Point Estimate :1: Margin of Error. But this is not the case when we construct condence intervals for a population variance. Why? Am This is because the distribution of tire sampling variance relates to tire (iii-square distribution, which is not symmetric