Which statement(s) is/are false about the Chi Square distribution?
A. As the degrees of freedom increases, the Chi Square distribution approaches a normal distribution.
B. The chi-square distribution is always right skewed, regardless of the value of the degrees of freedom parameter.
C. The chi-square statistic is always positive.
D. As the degrees of freedom increases, the shape of the chi-square distribution becomes more
What is that? The shape of a chi-square distribution curve is skewed for very small degrees of freedom, and it changes drastically as the degrees of freedom increase. Eventually, for large degrees of freedom, the chi-square distribution curve looks like a normal distribution curve. The peak (or mode) of a chi-square distribution curve with 1 or 2 degrees of freedom occurs at zero and for a curve with 3 or more degrees of freedom at d f - 2 df-2 The chi-square distribution has only one parameter, called the degrees of freedom. The shape of a chi-square distribution curve is skewed to the right for small of of and becomes symmetric for large of df. The entire chi- square distribution curve lies to the right of the vertical axis. The chi-square distribution assumes nonnegative values only, and these are denoted by the symbol x 2 x2 (read as "chi-square"). If we know the degrees of freedom and the area in the right tail of a chi-square distribution curve, we can find the value of x squared. 50, as you've gotten so used to me asking - where do we use this stuff in real life? What's a practical example? Thoughts? Ideas?Which of the following is NOT a property of the chi-square distribution? O A. The mean of the chi-square distribution is 0. O B. The chi-square distribution is different for each number of degrees of freedom, df = n - 1. O C. The chi-square distribution is not symmetric. D. The values of chi-square can be zero or positive, but they cannot be negative.2. You wish to test whether a coin lands \"heads\" and \"tails" with the same probability. Use p to denote the probability that the coin lands \"heads\". {a} State the relevant null and alternate hypotheses. [b] Suppose you choose to reject the null hypothesis when in 1G tosses you get more than T or less than 3 \"heads\". i. What is the power of your test when the true probability of \"heads\" is LIE? ii. What is the probability that your test results in a Type 11 error when the true probability of \"heads\" is I13? iii. Write an expression for the power function nip) of the test. iv. What is the size of the test? v. Make a plot of the power 1133) against 33 forp = {1131, 0.132, . . . ,D.QQ [Use R). vi. At what value of p is the power equal to the size? {0] Propose a test based on 21'} tosses which has size less than or equal to IIIJJE. {d} Plot the power curve of your tat
