The ruby-throated hummingbird beats its wings very quicky. Using a high-speed camera, an ornithologist was able to measure the wing beating speed (in beats per second) of 14 randomly chosen ruby-throated hummingbirds. The following are the measurements: 54.20, 51.99, 46.96, 50.91, 51.05, 45.75, 46.80, 50.57, 52.45, 48.41, 53.39, 51.97, 50.37, 51.41 Research has shown that wing beat speed is normally distributed. So, we assume that our sample comes from a normal population with an unknown mean of [4 and an unknown standard deviation of 0'. . We would like to test whether the average wing beat speed of ruby-throated hummingbirds is greater than 50 beats per second. The null hypothesis is thus H0:u=50 . We will test this against the alternative Ha . We want to test at the 6% level. Let )_( = the sample mean and s = the sample standard deviation. a) What should the alternative hypothesis, Ha , be? 0 Ha:y50 O Ha:,u=50 b) What is_the formula for your test statistic? x-SO O T = i 14 Eso O T = i 13 E-so O T = 5 'r' 13 O T = ; -5/o S E-so O T = 5 c) What value does your test statistic,T, take on with the sample data? |:] d) What type of probability distribution does your test statistic,T, have? 0 t O Cauchy O Chi-Squared 0 normal 0 binomial e) How many degrees of freedom does T have? f) Calculate the critical value, tstar, for your test.(positive value) g) For what values of your test statistic, T, is the null hypothesis rejected? O T > tstar/2 or T tstar or T tstar h) Calculate the p-value for this test. i) Is the null hypothesis rejected? (Y/N) ON OY j) If we ran 800, 6% level tests then about how many times would we make a Type I error? k) Create a 94% confidence interval for the average wing beat speed of ruby-throated hummingbirds based upon the above data (