8.23 Chicken breast In a 2014 Consumer Reports article titled, “The High Cost of Cheap Chicken,” the magazine reported that out of 316 chicken breasts bought in retail stores throughout the United States, 207 contained E. coli bacteria.

a. Find and interpret a 99% confidence interval for the population proportion of chicken breasts that contain E. coli. Can you conclude that the proportion of chicken containing E. coli exceeds 50%? Why?

b. Without doing any calculation, explain whether the interval in part a would be wider or narrower than a 95% confidence interval for the population proportion.