Question

As the quality engineer for a small chain of fast food restaurants called McDowell’s (They’ve got the Big Mac, we’ve got the Big Mick), you’re interested in describing the consistency of the foodstuffs at a particular branch. In particular, you want to develop graphical and numerical representations of the (i) weight of and (ii) number of fries in a small bag of McDowell’s fries. You’ll find a sample of 32 bags in the below table.

a. Provide numerical descriptions of the weights and numbers of fries in the sample.

b. Calculate and interpret 95% confidence intervals for the weight of a bag of small fries and the number of fries in a bag of small fries.

c. If the target value set by McDowell’s for the weight of a small order of fries is 2.61 ounces, what might you conclude based on your sample?

d. As a quality control engineer, what could you do with such information?

Observation	weight (oz)	number of fries
1	2.22	30
2	2.38	43
3	3.66	54
4	2.51	70
5	2.28	40
6	2.39	45
7	2.7	46
8	2.98	55
9	2.93	41
10	2.13	40
11	2.14	36
12	2.7	50
13	2.51	52
14	2.45	42
15	2.22	46
16	2.45	43
17	3.27	58
18	2.51	53
19	2.15	37
20	2.23	42
21	2.29	39
22	2.94	55
23	2.72	56
24	2.81	44
25	2.74	56
26	2.92	53
27	2.08	36
28	2.54	52
29	2.71	56
30	2.98	66
31	2.74	51
32	3.1	53

Answer 1

a.

Descriptive Statistics: weight (oz), number of fries

Variable Mean StDev Q1 Median Q3 Mode
weight (oz) 2.6056 0.3708 2.2825 2.5250 2.8925 2.51   
number of fries 48.13 8.98 41.25    48.00 54.75 53, 56

From above we see that weight is positively skewed (Mean>median and see box plot) and number of fires is almost symmetric (see box plot).

From above probability plots, we see that weight and no. of fires both follow normal distribution.

b.

One-Sample T: weight (oz), number of fries

Variable N Mean StDev SE Mean 95% CI
weight (oz) 32 2.6056 0.3708 0.0655 (2.4719, 2.7393)
number of fries 32 48.13 8.98 1.59   ( 44.89, 51.36)

We are 95% confident that the true mean weight lies between 2.4719 oz and 2.7393 oz.

We are 95% confident that the true average no. of fires lies between 44.89 and 51.36.

c.

Since 2.61 oz falls in the 95% CI for the true mean weight so if the target value set by McDowell’s for the weight of a small order of fries is 2.61 ounces, then we are 95% confident that we can reach this target.

d. Using the above information, we can control the quality.