T9. As kitten season is coming up (yes that is a real thing), the number of newborn kittens found outside without their mom increases during this part of the year. Suppose the Hayward Humane Society has taken in 70 kittens. They gave 10 fosters each 7 kittens. The fosters collect the weight of each of their 7 newborn kittens and calculate the mean weight for their litter. Let the random variable SXS = the weight of a newborn kitten. Label each description as either a population, sample, or sampling distribution. a. The distribution of all newborn kitten weights. b. The distribution of 10 mean weights of newborn kittens from each foster's litter. c. The distribution of 7 newborn kitten weights cared for by a single foster. Recall the Bechdel dataset. ([Link](https://github.com/rfordatascience/tidytuesday/tree/master/data/2021/2021-03-09]]. 10. [5 points] Using the data, perform a 5-step hypothesis test to determine if the percentage of movies that pass the Bechdel test in 2013 is greater than 501%. Extra Credit [5 points]. The CLT (for means) states that if we have a random sample 5X_1, X 2, \\cdots, X_n loversetfid)(\\sim] N[\\mu, \\sigma]S, then 5\\bar(X) = \\frac(1Hn/\\sum_(1=1)^n X_/\\dot[\\sim] N[\\mu_[\\bar(x]] = \\mu, \\sigma_[\\bar(x]] = \\frac[\\sigma][\\sqrt(n]]IS. Prove SE[\\bar[X]] = \\mu$ and SSD[\\bar(X]] = \\fract\\sigmal\\sqrtin]IS