Question

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 40 cookies. The mean is 23.47 and the standard deviation 2.83. Construct a 98​% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies. Also, please explain how to use a calculator with this example.

Answer 1

A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 40 cookies. The mean is 23.47 and the standard deviation 2.83.

Confidence Interval is a range of values we are fairly sure our true value lies in.

Calculating the Confidence Interval

Step 1: find the number of observations n, calculate their mean , and standard deviation

Using our example:

• Number of observations: n = 40
• Mean: = 23.47
• Standard Deviation: = 2.83

Step 2: decide what Confidence Interval we want: 98%. Then find the "Z" value for that Confidence Interval in Normal Distribution table or through a brief from of it given below

Confidence Interval	Z
80%	1.282
85%	1.440
90%	1.645
95%	1.960
99%	2.576
98%	2.33
99.9%	3.291

For 98% the Z value is 2.33

Step 3: use that Z in this formula for the Confidence Interval

±  

And we have:

23.47 ± 2.33 × 2.83/√40 = 23.47 ± 1.0426

22.4274 24.5126