Question

"Heinz Plays Catch-up After Under-Filling Ketchup Containers" is the headline of an article that appeared on CNN.com (November 30, 2000). The article stated that Heinz had agreed to put an extra 1% of ketchup into each ketchup container sold in California for a 1-year period. Suppose that you want to make sure that Heinz is in fact fulfilling its end of the agreement. You plan to take a sample of 20-oz bottles shipped to California, measure the amount of ketchup in each bottle, and then use the resulting data to estimate the mean amount of ketchup in each bottle. A small pilot study showed that the amount of ketchup in 20-oz bottles varied from 19.8 to 20.5 oz. How many bottles should be included in the sample if you want to estimate the true mean amount of ketchup to within 0.1 oz with 95% confidence? (Give the answer to the next largest integer.)

Answer 1

we have the margin of error (ME) = 0.1 and z score for 95% confidence interval is 1.96

we have to find the sample size(n)

the formula for sample size is given as n =

so, we need to find the value of standard deviation

we have the range from 19.8 and 20.5

Using the range rule of thumb, we know that the = range/4

so, = (20.5-19.8)/4 = 0.7/4 = 0.175

Now, we have , ME and z value to put in the sample size(n) formula

we get

n =

rounding off to nest largest integer, we get 12

so, Required sample size is 12