Question

8.23 A manufacturing company produces chocolate bars. The table below contains the cost per ounce ($) for a sample of 14 dark choco- late bars. 0.63 0.79 0.95 1.19 1.45 0.94 0.78 0.53 1.58 0.53 0.61 0.73 1.52 0.81 a. Construct a 99% confidence interval estimate for the popula tion cost per ounce ($) of dark chocolate bars. b. What assumption do you need to make about the population distribution to construct the interval in (a)? c. Given the data presented, do you think the assumption needed in (a) is valid? Explain

Answer 1

a) The first step to the question is to find out the Mean and the SD of the Population, which is calculated as below:

SI No Cost per Ounce Dev=X-Mean Dev^2 0.63 -0.30 0.79 -0.14 0.95 0.02 1.19 0.26 1.45 0.52 0.94 0.01 0.78 -0.15 0.53 -0.40 1.58 0.65 0.53 -0.40 0.61 -0.32 0.73 -0.20 1.52 0.59 0.81 -0.12 13.04 0.93 0.09 0.02 0.00 0.07 0.27 0.00 0.02 0.16 0.42 0.16 0.10 0.04 0.35 0.01 1.72 14 Total Mean 1.72 Sum of Squared Deviations around Mean n-1 Variance 0.13 SD 0.36

The next step is finding out the z-score @ 99% confidence interval which is 2.58.

Finally, we construct the Confidence Interval (CI) which is represented by

CI = Mean +/- z*SD/(SQRT(n))

33 1.18 | 0.68

Applying the formula, we have now constructed the Confidence Interval with Upper Limit(UL) and Lower Limit (LL).

b) There are a few important assumptions made, such that the distribution is a normal distribution and that the samples are constructed randomly and that they are independent of each other.

c) The assumption may pose challenges for smaller samples and will tend to hold for larger sample sizes