The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = EK.P(X = k) k 1 2 3 4 5 6 7 (or more) PIX=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %Ciara, an ornithologist (a person who studies or is an expert on birds.), has 4 bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders (each expected proportion to be 25%) . She recorded data for a sample of 350 recent visits. Here are the results: Feeder #1 #2 #3 #4 Observed visits 80 90 92 88 HINT: Use Rguroo: Analysis-> analytics-> Goodness of Fit: Make 4 levels (categories) - complete observed counts using the values in the table - for null probabilities check Ho If Ciara performs a goodness-of-fit, can she determine if these results suggest that birds visit one specific feeder is different or the same from the other feeders. Test at 5% significance level. Ho : P1 = P2 = P3 = P4 = 25% Ha : At least one proportion is different than expected. a) The value of the observed test statistic is Xobserved = Round to two decimal places. b) The Xcritical = Round to two decimal places. c) Result: Since Xobserved Xcritical we fail to reject the null. (use the operations ">" or "