Question

1. Win Dixie distributes pineapple chunks in 4.5 ounce plastic cups. To ensure that each cup contains at least the required amount, Win Dixie sets the filling operation to dispense 4.51 ounces of pineapples. The filling process follows a normal distribution. The quality control technician selects a sample of 4 cups at the start of each shift, measure the amount in each cup and develops a 95% confidence interval for the population mean.

The fill amount of 4 cups collected at 6 a.m. this morning are as follows:

4.507                4.494               4.502               4.481

1. Calculate the standard deviation for the sample of 4 cups.
2. Develop a 95% confidence interval for the population mean fill amount (hint: be careful which distribution you will use for the critical value).
3. Using the confidence interval, is the process filling the cups to the desired amount?
4. What suggestion would you give the technician in order to improve the reliability of the test?

Answer 1

a)

А в s.Dev 4.507 4.494 4.502 4.481 0.011343 4.496 mean

b)

The critical value for a = 0.05 and df = n-1=3 degrees of freedom is te = %1-a/2:n-1 = 3.182. The corresponding confidence interval is computed as shown below: CI = (x-te x 8 +tex in) = (.196 – 3.182 007, 1.96 + 3.182004) = (4.478, 4.514)

c) 4.51 lies within the interval calculated above hence we can say that the the process filling the cups to the desired amount.

d)the technician should take a bigger sample greater than or equal to 30 in order to improve the reliability of the test