Name_______________________ STA 6166 Homework #3 Spring 2005 1. The incidence of paratuberculosis (Johne’s disease) in Florida beef cattle is about 10%. a. You test a sample of 50 animals from a large herd and find 7 infected. Does this make you believe that the herd has a higher incidence than the state incidence? Why or why not? (Compute the probability of 7 or more infections if the true incidence were .1.) b. You test a sample of 50 animals from another large herd and find 10 infected. Does this make you believe that this herd has a higher incidence than the state incidence? Why or why not? (Compute the probability of 10 or more infections if the true incidence were .1.) 2. You are testing honeybees for transport to possible shipment to Pennsylvania for establishment of new colonies. The buyer does not want to any infected bees in the purchase. However, the only way to insure that is to test every bee, which is impractical. You want to be 90% confident that there no more than .1% are infected. How many bees would you have to test to attain this level of confidence?3. Each time you purchase gasoline, you calculate the miles per gallon you got on the previous tank fill. Here are the mpg values for your previous 16 fills: 20.4 22.1 21.7 25.3 22.6 25.3 21.2 22.4 21.8 23.7 22.1 22.6 23.5 21.2 23.1 24.6 Consider these mpg values to be a random sample from the conceptual population of mpg values you would get from driving this car under similar conditions for a very long time. Letµ and2yσ denote the mean and variance, respectively, of this population. a. Compute estimates ofµ and2yσ. b. Draw a graph that depicts the distribution of the population of mpg values from which your sample of date was obtained.c. Compute an estimate of the variance 2yσ of the sampling distribution of means of 16 observations each. d. Draw a graph that depicts the sampling distribution of means of 16 observations each. e. Construct an interval that you are 95% confident contains the mean mpg for your
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