The irradiation of food to destroy bacteria is a growing phenomenon. In order to determine which one of two methods of irradiation is best, a scientist took a random sample of 100 one- pound packages of minced meat and subjected 50 of them to irradiation Method 1 and the remaining 50 to irradiation Method 2. The bacteria count was measured and the following statistics were computed. The scientist noted that the data are normally distributed. NOTE: use ONLY the Critical Value method for hypothesis tests. If you include both rules in step 4 or include both in your decision step, I will have to conclude that you do not yet understand them. Method 1

 x ̄_1=86 

s_1^2=324 

Method 2 

x ̄_2=98 

s_2^2=841

a.) Estimate with 99% confidence the mean bacteria count with Method 2. Interpret the interval.

b.) Can we conclude at the 5% significance level that the variance of the bacteria count with Method 2 is less than 1,500?

c.) An important factor in determining which method to choose is consistency. That is, all other things being equal we’d prefer a method that leaves all irradiated food with approximately the same bacteria count. Can we infer at the 1% significance level that Method 1 is superior to Method 2 in this respect?

d.) Estimate with 95% confidence the variance of bacteria count with Method 1. Interpret the interval.