Question

1. In a random sample of ten 35 g "Fruit & Nut" trail mix bars, the average total fat content is found to be 4 g with a standard deviation of 0.5 g. Assuming all assumptions for inference are met, what is a 90% confidence interval for the mean total fat content of such trail mix bars 2. Of the 125,000 "senior" males playing on their school varsity baseball teams, 120,000 are in high school and 5,000 are in college. Suppose that 0.2% of such high school players are drafted by MLB teams, while 10.5% of such college players are drafted. If a player is drafted, what is the probability the player is from high school? 3. It is universally accepted that inactivity heightens chronic disease rates. A recent study concluded that 30% of U.S. adults are not getting the recommended level of exercise. In a random sample of U.S. adults, if the first three surveyed are not getting the recommended level of exercise, what is the probability that the next two surveyed also are not getting the recommended level?

Answer 1

1)

Level of Significance ,    α =    0.1          
degree of freedom=   DF=n-1=   9          
't value='   tα/2=   1.833   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   0.5000   / √   10   =   0.1581
margin of error , E=t*SE =   1.8331   *   0.1581   =   0.2898
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    4.00   -   0.289841   =   3.7102
Interval Upper Limit = x̅ + E =    4.00   -   0.289841   =   4.2898
90%   confidence interval is (   3.710   < µ <   4.290   )