STATISTICS - Problem Group I

Instructions: Read each of the following problems, then decide what procedure to follow to properly complete the problem.

1. The U.S. National center for Health Statistics estimates mean weights of Americans by age, height, and sex and publishes the results in Vital and Health Statistics.   Forty U.S. women, 5ft 4in tall and age 18-24 yrs, are randomly selected.   Their weights, in pounds, has a mean of 136.9 lbs and s = 12.77 lbs. 

                a)   Find a 90% confidence interval for the mean weight, µ, of all U.S. women 5ft                      4in tall and in the age group 18-24 years.

                b)   Interpret your result in part (a).

    2.  According to Food Cost Review, published by the U.S. Department of Agriculture, the average retail price for oranges in 1983 was 38.5 cents per pound.  Recently, 15 randomly selected markets reported prices for oranges that average 40.8 cents per pound, with s = 3.38 cents per pound.  Can we conclude that the mean retail price for oranges now is different from the 1983 mean of 38.5 cents per pound?  (A normal probability plots indicates the distribution of the sample data is approximately normally distributed.)

    3.  As reported by the Department of Agriculture in Crop Production, the mean yield of oats for U.S. farms is 58.4 bushels per acre.  A farmer wants to estimate his mean yield using a newly developed fertilizer.  He uses the fertilizer on a random sample of 1-acre plots and obtains the yields with a mean of 61.5 bushels per acre, s = 3.38 bushels per acre.  Does it appear that the farmer can get a better mean yield than the national average by using the new fertilizer?   (Assume the distribution is approximately normal.)

    4.  A dog-food manufacturer sells '50-lb' bags of dog food.   Suppose you randomly select 75 bags and find a mean = 50.1 lb and s = 0.84 lb.   Would you be inclined to believe that the actual mean weight of all '50-lb' bags of this dog food differs from the advetised weight of 50 lb?  (Use a 5% significance level.)

    5.  A random sample of 10 Kansas families of four with intermediate budgets yielded the data in 1984 weekly food costs shown below.  Do the data provide sufficient evidence to conclude that in 1984, the mean weekly food cost for Kansas families of four with intermediate budgets was less than the national mean of $92?   (Use a 5% significance level, and assume the population is symmetric.)

                $     78    104    84    70     96    73    87    85     76    94

Which Procedure Should You Use?